LATE AND ABSENT HOMEWORK IS ACCEPTED UP TO THE TIME OF THE CHAPTER TEST ON

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1 Trig/Math Aal Name No LATE AND ABSENT HOMEWORK IS ACCEPTED UP TO THE TIME OF THE CHAPTER TEST ON HW NO. SECTIONS ASSIGNMENT DUE SS / Practice Set A #7 Practice Set J # 0 SS Practice Set A #,, 8 Recursive Practice Set B #7,, 7 (Brow) Practice Set L # odd,,, SS / Practice Set B #,, Practice Set J # 7 SS Practice Set B # Practice Set J #8, 6, 66 Practice Set L #0 SS ( B) Review SS 6 6 SS 7 7 SS 8 SS PMI PMI Practice Set C # Practice Set D #,, Practice Set G #, 0 Practice Set J # 6 Practice Set L #, 8 Practice Set B #, 0 Practice Set C #, Practice Set D # Practice Set F #7 Practice Set G #, 7 Practice Set H #, 6 Practice Set J #67 70 Practice Set L #, 6 Practice Set D #7,, 6 Practice Set E #6, 0, Practice Set F #6, 8 Practice Set G #, 8,, Practice Set H #, 0 Practice Set J #7 76 Practice Set B # Practice Set C #, 7 Practice Set F # Practice Set G # Practice Set H #8 Practice Set K # Practice Set L #6 Practice Set G #, Practice Set H #, Practice Set K # 8 Practice Set L #0, - -

2 HW NO. SECTIONS ASSIGNMENT DUE Practice Set A #0 Practice Set B #, ( 6B) Practice Set C #8 SS 0 Review Practice Set E # Practice Set F # Practice Set K # SS ( 7B) Review Practice Set B #8, 8 Practice Set D #, Practice Set E # Practice Set G # Practice Set H #0, 7 Practice Set J #77 86 Practice Set K #6, 8, 0 - -

3 Practice Set A. Fid the first eight terms of the sequece i which a =, a =, ad a = a + a for =,, Fid the first six terms of the sequece i which a =, a =, ad a = a + a for =,, + + For Exercises 6 a. Write the sequece whose terms are obtaied by performig the idicated operatio o the terms of the arithmetic sequece,,, b. Is the resultig sequece a arithmetic progressio? Explai.. Multiply each term by. Multiply each term by 0. Square each term. Subtract from each term. Multiply each term by a ozero real 6. Add a real umber k to each term umber k 7. For what value(s) of x will x +,x+, ad x, i this order, form a arithmetic sequece? 8. If a, a, a is a arithmetic progressio, show that a + a6 = a + a = a Practice Set B Fid the value of a for the give values of a, d, ad i a arithmetic sequece.. a =, d =, =. a =, d =, = 0. a =, d =, = 7. a =, d =, =. a = 6, d = 0, = 8 6. a =, d = 7, = 00 Fid the specified term a of the idicated arithmetic sequece. 7.,8,; a 6 8.,8,; a 6.,,; a 0. 6,, ; a.,,; a.,, ; a.,.,0; a0..00,0.,0.0; a 0 Isert the stated umber of arithmetic meas betwee the give umbers.. Three betwee ad 6. Seve betwee ad 7. Five betwee 8 ad 8. Te betwee ad. Three betwee 8 ad 0. Seve betwee ad Fid the missig terms i the idicated arithmetic sequece..,,,,.,, 0,,., 0,,,.,,,, 7., 7,,, 6.,,,, 0 7. Which term of the arithmetic sequece,, is? 8. Which term of the arithmetic sequece,, 6 is?. For what value of x is the arithmetic mea of x ad x? 0. For what value of y is the arithmetic mea of y 8 ad y+ 6?. For what value of s is s the arithmetic mea of ad s + 7?. For what value of t is t the arithmetic mea of 7 t ad t? Practice Set C. A editor takes a positio at $700 a year. She receives aual icreases i salary of $0. What will her salary be durig her twelfth year of service? - -

4 . A youg ma s aual salary icreased for six years i arithmetic progressio. If his salary the first year was $600 ad his salary the sixth year was $800, what was his salary durig each of the other years?. A Vacatio Savigs Club which helps members to save moey for their vacatios requires each member to deposit $0 the first week ad to icrease his deposit by $ weekly for eleve weeks. How much is the fial (twelfth) deposit?. Mr. Ad Mrs. Fritz ope a savigs accout whe their daughter is i the fifth grade to provide for her college educatio. If they deposit $00 the first year ad icrease their deposits by $0 each year after that, how much will they deposit whe their daughter is i the 0 th grade?. The seve weights i a set for a aalytic balace are i arithmetic progressio. If the ext to heaviest is grams ad the lightest is gram, what are the other weights? 6. Some boys o the beach decide to form a huma pyramid havig oe perso fewer i each successive layer. If there are boys i the bottom (or first) layer, how may are i the fifth layer? 7. The aual cost of repairs after the first year for a certai automobile icreases $70 each year. If the cost of repairs durig the first year is $, how much will be spet o repairs durig the 6 th year? 8. Joh repays some moey that he owes his sister by makig mothly paymets. The first paymet is $ ad every succeedig paymet is $ more tha that of the precedig moth. How much does he give his sister the 0 th moth?. A studet takig a test cosistig of te questios is told that each questio after the first is worth two credits more tha the precedig questio. If the third questio is worth fiftee credits, how much is the last questio worth? 0. A builder fids that his profit from the sale of the first house i a developmet is $00 (he loses $00). His profit o the sale of the secod house is $0. O sellig more houses i the developmet, he fids that each additioal house sold icreases his profit per house by $0. How may houses did he sell if his profit o the last house was $600?. A woma drivig alog a iterstate toll road at 0 kilometers per hour ( meters per secod) applies the brake as she approaches a tollbooth ad comes to a complete stop i secods. If the speed at which she is travelig at the ed of successive secods falls off i arithmetic progressio, how fast was she travelig at the ed off the twelfth secod after brakig?. At the ed of oe year, the trade i value of a certai automobile is $700 less tha the origial cost. Each year thereafter the trade i value decreases by $0. If the origial cost of the automobile is $00, what is the trade i value at the ed of years? Whe is the trade i value 0? Practice Set D Fid the sum of the arithmetic progressio havig the give data.. a = 8, a = 8, = 6. a =, a = 7, = 8. a =, a =, =. a = 0, a =, = 7. a =, d =, = 8 6. a = 7, d = 6, = 0 7. a = 8, d =, = 8. a = 0, d =, = Write each of the followig expressios i summatio otatio Fid the secod term of the arithmetic series havig the give data.. d =, =, S =. d =, = 0, S = 0 - -

5 . a =, a = 0, S = 6. a = 0, a = 8, S = Practice Set E. I a psychology lecture hall there are 7 seats i the first row ad seats more i each followig row. How may seats are there i the frot rows?. How much did a evirometal egieer ear i te years if her startig salary was $,00 ad she received aual icreases of $60?. The clock i a courthouse tower chimes as may times as the hour. How may times does it chime betwee 7:00 am ad 6:00 pm iclusive?. If the taxi rate is 0 for the first kilometer ad 0 for each additioal kilometer, what is the fare from dowtow to the airport, 0 km away?. If a state icome tax is % o the first thousad dollars of et icome, % o the secod thousad, ad so o i arithmetic progressio, what is the total tax paid o a et icome of $,000? 6. Juaita wet to work as a teller i a bak at a salary of $600 per year, ad received yearly icreases of $00. If she saved 0% of her icome how much had she saved after 7 years? 7. Fid the sum of the positive three digit itegers that are divisible by. 8. A well drillig firm charges $.00 to drill the first meter, $.0 for the secod meter, ad so o i arithmetic progressio. At this rate, how much does the firm charge to drill a well 0 meters deep?. Fid the sum of the positive itegers that are less tha 00 ad are divisible by. 0. Fid the sum of the positive itegers that are less tha 00 ad are ot divisible by.. Sue Smith ad Jack Rogers started to work at the same time ad at the same yearly salary. Sue s employer agreed to icrease her salary $00 per year at the ed of every half year, while Jack s boss agreed to raise his salary $600 per year at the ed of each year. By how much did Sue s total salary exceed Jack s over a te year period?. Fid the sum of the itegers betwee 00 ad 00 that are divisible by 7. Practice Set F. If you were give a gift of $ o your first birthday, ad the gift was doubled o each followig birthday, how much would you receive o your twety first birthday? (Hit: Use the fact that ( ) = = 6 0. How may acestors of the eleveth geeratio does a perso have assumig that there is o duplicatio?. There are seve forests. I each are seve owls. Each owl kills seve mice. Each mouse would have eate seve ears of cor. Each ear of cor will produce seve measures of grai. How much grai is saved?. A large compay has a telephoe commuicatio system i the evet of a blizzard i which oe perso calls five persos of Group A, each of whom the calls five persos of Group B. Each of these twety five persos the calls five persos of Group C, ad so o through Groups D ad E. How may persos are there i Group E?. A ma seds out four letters o Saturday with istructios to the recipiets to write letters to two frieds o the followig Saturday, askig them to do likewise. If there are o duplicatios ad o oe breaks the chai, how may letters are set o the sixth Saturday? 6. The value of a certai rare coi icreases by oe teth each year. If the coi is worth $.00 ow, what will be its approximate value i years? - -

6 7. A side of a equilateral triagle is 6 cetimeters log. A secod equilateral triagle is iscribed i it by joiig the midpoits of the sides of the first triagle. The process i cotiued. Fid the perimeter of the sixth iscribed equilateral triagle. 8. A tak cotais 000 cubic cetimeters of gas. O its first stroke, a pump removes of the gas, leavig of 000 cubic cetimeters of gas i the tak. O the secod stroke, the pump removes of the remaiig gas, ad so o. How much gas is left i the tak after the sixth stroke of the pump? I exercises use the followig compoud iterest law: P dollars earig iterest at r % r 00 per year compouded d times a year amouts to r P + at the ed of oe year ad 00d d r to P + at the ed of years. 00 d. Explai why the successive amouts computed at the ed of each iterest period accordig to the compoud iterest law form a geometric progressio. What is the commo ratio of the progressio? 0. The iterest rate i a certai bak is 8% compouded semiaually. If you deposit $0,000 i a accout ad make o other deposits or withdrawals, how much moey will be i your accout at the ed of two years?. Fid the compoud iterest due at the ed of years if $000 is ivested at 0% compouded aually. Practice Set G Isert the give umber of real geometric meas betwee the give umbers ad write the resultig geometric sequece. Give all possible correct aswers. 7. Two betwee ad 8. Two betwee ad 7. Two betwee ad 0. Two betwee 6 ad 6. Three betwee ad 8. Three betwee ad 7. Three betwee ad. Three betwee 8 8 ad. Which term i the geometric progressio,, is 6 6. Which term i the geometric progressio 80,0, is 7. The first term of a geometric sequece is 6, the commo ratio is ad there is a term a =. What is the value of? 8. If the first term of a geometric sequece is ad the commo ratio is, for what value of is a = 80?. If the third term of a geometric sequece is ad the commo ratio is, what is the ith term? 0. The fifth term of a geometric sequece is ad the commo ratio is. What is the first term?. The seveth term of a geometric sequece is 87 ad the fifth term is 7. What is the first term?. If the fourth term of a geometric sequece is ad the seveth term is 6 8, what is the third term?? 6? d - 6 -

7 . A dealer bought a paitig for $0,000 ad three years later sold it for $6,60. Assumig that the value icreased geometrically each year, fid the average rate per year at which the value of the paitig icreased.. A ivestor purchased some Amalgamated Petroleum Eterprises stock for $0,000 ad two years later sold it for $,68. Assumig that the value decreased geometrically each year, fid the average rate each year at which the value of the stock decreased.. Show that if b is the geometric mea of a ad c, the b is the geometric mea of a ad c. 6. From the result of Exercise, deduce that the squares of the terms of a geometric progressio also form a geometric progressio. 7. Show that the reciprocals of the terms of a geometric sequece i which a 0 ad r 0 also form a geometric sequece. Practice Set H Fid the sum of the terms of the idicated geometric sequece..,6,8, to terms.,0, 0, to 6 terms., 0, 0, to 6 terms., 6, 08, to terms.,,6, to 6 terms 6.,,, to 6 terms 7. 7,,, to 8 terms 8.,,, to 7 terms Fid the sum of the give geometric series. i. ( ) i= ( ) 6 i= i k. ( ). ( ) k = j. j=. ( ) k = 0 j j= I Exercises 6 three of the five real umbers a, a, r,, ad S for a geometric sequece are give. Fid the two umbers that are ot give.. a = 8, r =, = 6. a =, r =, = 7 7. a =, r =, = 8. a,, = r = =. r =, =, S = 0 0. r =, =, S = 00. a =, r =, S =. a =, r =, a = a =, a = 8, S =. a = 6, a =, = 6 k 7. a =, =, S = 6. a =, =, S = Practice Set J Fid the specified term of each arithmetic sequece: 8,,6,...;t,,,...;t t = 0, t = 6; t.. Fid the specified term of each geometric sequece: 6,6,,...;t t = 6, t = 0; t... Isert the give umber of arithmetic meas: 6a. oe, betwee 8 ad. 6b. five, betwee ad 6 Tell whether each sequece is arithmetic, geometric, or either. The fid a formula for the th term:

8 7.,,,,... 8.,,,,,.... The sequece of egative eve itegers that are multiples of. 0. Fid the positio,, of i the arithmetic sequece: 7,6,,...,,. How may umbers betwee 0 ad 00 are divisible by 7? Tell whether each sequece is arithmetic, geometric, or either. The supply the missig terms of the sequece:. 7,,,,,.,,, 6,,,,,,. Fid the first four terms of the give sequece ad tell whether the sequece is arithmetic, geometric, or either:. t = 6. t = log 0( + ) Fid the ext two terms of each sequece by aalyzig the patter of the differeces: 7.,,,,,... 8.,,7,,,....,,,,,8,,... (This well kow sequece is called the Fiboacci sequece.) Write each series i expaded form: ,,6,,,,... (Look at the differeces of the differeces.) +. =. = Write each series usig sigma otatio: Write each series usig sigma otatio: k k= j=. Fid the value of Fid the sum of each arithmetic series: 0. = 0, t =, t0 = ( k + ). k = 0 Fid the sum of each geometric series:. =, = 6, t. =, t = 8. Write the first three terms of this arithmetic series: t =, S = 68 whe t = 78 Fid the sum of the elemets of the give set: 6. The positive two digit itegers edig i 7. The positive three digit itegers divisible by 6 Fid the sum of the elemets of the give set: 8. The positive a. The first twety b. The first twety 0. The positive twodigit three digit odd multiples of, startig powers of, startig itegers that are itegers with with ot divisible by. The frot row of a lecture hall has 7 seats. There are two more seats i each followig row. How may seats are there i the first 0 rows?

9 . Some bricks are stacked so that there are bricks i the top row ad more bricks i each successive row dow to the groud. If there are rows i all, how may bricks are there i the whole stack? For each ifiite geometric series, fid the sum if the series has oe. If it does ot, say so: Write the first three terms of the ifiite geometric series satisfyig the give coditio: 6. t =, S = r = 0.8, S = 7. Express each repeatig decimal as a commo fractio by rewritig each as a ifiite series: Each year a certai type of tree grows vertically as much as it did the year before. If the tree grows.m durig the first year, how tall will it ultimately grow?. A side of a square is cm. The midpoits of its sides are joied to form a iscribed square, ad the process is cotiued as show i the diagram. Fid the sum of the perimeters of the squares if this process is cotiued without ed.. Fid the sum of the areas of the squares i Problem.. A rubber ball dropped from a height of 0 cm rebouds o each bouce to a height which is of its height o the previous bouce. How far will it travel before comig to rest? Fid the specified term of each sequece: a.,,,...;t 8 0,,,...; t b. 7 Fid a formula for the th term of each sequece: a. 8,,7,...,,,,... c. 6,8,,... b Fid the geometric mea of 8 ad A discout store reduces its prices each week by 0% of the previous week s price. A coat priced at $0 durig the first week was sold durig the fourth week. At what price was the coat sold? 8. Write usig sigma otatio: A arithmetic series cosistig of eleve terms with first term 8 ad last term 08. For each ifiite geometric series, fid the sum if the series has oe. If it does ot, say so: Express each repeatig decimal as a commo fractio by rewritig each as a ifiite series: I the first back ad forth swig of a pedulum the bob traveled 6 cm. I each subsequet swig the bob travels % as far as i the precedig oe. How far does the bob travel before comig to rest? 6. A side of a equilateral triagle is 0 cm. The midpoits of its sides are joied to form a iscribed equilateral triagle ad the process is cotiued. Fid the sum of the perimeters of the triagles if the process is cotiued without ed. 6. The Allisos have bee retig a house for the past years. Durig the first year of retal, they paid $00 a moth, ad each year thereafter their ret was icreased by 0%. Fid the total amout they have paid for ret over the last years. - -

10 66. The maagemet of a large bak cosists of a presidet, vice presidets, maagers, ad so o, dow through 6 levels of maagemet. How may people are ivolved i the 6 levels? 67. Two studets are readig a historical ovel. Oe reads 0 pages a day ad the other reads 0 pages the first day, 0 the secod, 0 the third, ad so o. After how may days will they be o the same page? Expad each expressio: 68. ( p + )8 6. ( a + )6 Write the first four terms i the expasio of each biomial: 7a. ( a+ b )0 7b. ( a b )0 7a. ( a+ b ) Fid ad simplify the specified term i each expasio: ( 7 a + b 70. ) 7b. ( x y ) 6 7. The term cotaiig b i ( a+ b )0 7. The eleveth term of ( s+ t ) Fid ad simplify the specified term i each expasio: 7. The term cotaiig a i ( a+ b ( ) c d 76. The middle term of )8 00 t = ( ) 77. Fid the first four terms of the sequece with th term ad tell whether the sequece is arithmetic, geometric, or either. 78. Fid the sixth term of the sequece,,, ,,,, Fid a formula for the th term of the sequece Isert three arithmetic meas betwee ad Use sigma otatio to write the series 8. Fid the sum of the first twety terms of the arithmetic series Evaluate = 8. Fid the sum of the ifiite geometric series if it has oe. ( s+ t ( 8. Expad ad simplify ) w+ y 86. Fid the fourth term i the expasio of )6 Practice Set K: Mathematical Iductio Prove true by iductio. ( ) ( ) = = = b g = + + is 7. Expad bx yg 8. Write the first four terms of x+ y Prove true by iductio. b + gb+ g = 6 is. ( + + ) is 6. ( ) = + b g b g b g =. ( ). ( ) is = is 7 6. ( ) b g. ( ) + + is

11 7. ( ) + is 8. ( ) b g 0. is = = Practice Set L ( Brow) Fid the third, fourth, ad fifth terms of each sequece.. t = 6; t = t +. t = ; t = t. t = ; t = t. t ( ) = ; t = t 0. t = ; t = t + 6. t = ; t = ( t + ) + 7. t = ; t = ; t = t + t 8. t = ; t = ; t = t t. t ( ) = ; t = 8; t = t t 0. t = 7; t = ; t = t t. Fid a explicit defiitio for the sequece i Exercise. Fid a explicit defiitio for the sequece i Exercise Give a recursive defiitio for each sequece..,, 7,,.... 8, 7,,,....,, 7,,, 6,... 6.,, 7,,,,... 7.,, 6, 0,,,... 8.,, 6,, 0, 70,... a. Give the first eight terms of the sequece defied recursively by t =, t =, ad t = t t. b. Observig the patter you get i part (a), tell what the 000 th term of the sequece will be. t 0a. Give the first eight terms of the sequece defied recursively by t =, t = 8, ad t =. t 0b. Observig the patter you get i part (a), tell what the 000 th term of the sequece will be.. Geography. Suppose the populatio of those livig i the coutry grows % per year, ad that a additioal 0,000 people immigrate ito the coutry every year. a. Give a recursio equatio for P, the populatio i years. b. If the populatio ow is 8,00,000, what will the populatio be i years?. Chemistry. Each day 8% of a quatity of radioactive iodie will decay. a. Express this fact with a recursio equatio. b. Choosig a value for the iitial amout of iodie, fid the approximate half life of the iodie.. Visual Thikig Let S represet the umber of dots i a by square array. Preted you have forgotte that S =. Give a recursio equatio that tells how S + is related to S by reasoig how may extra dots are eeded to form the ( + ) st square array from the previous th square array. Illustrate your aswer with a diagram of dots.. Suppose that everyoe i a room shakes hads with everyoe else exactly oce. Let H represet the umber of hadshakes if there are people ( ) i the room. Give a recursio equatio that tells how H is related to H. (Hit: Suppose you kow H. If aother perso eters the room, how may additioal hadshakes will there be?) - -

12 . Fiace. O the birth of their daughter, Mr. ad Mrs. Swift bega savig for her college educatio by ivestig $000 i a auity accout payig 0% iterest per year. Each year o their daughter s birthday they ivested $000 more i the accout. a. Let A represet the amout i the accout o their daughter s th birthday. Give a recursive defiitio for A. b. Fid the amout that will be i the accout o her 8 th birthday.. Physics. Newto s Law of Coolig states that over equal time periods (for example, oe miute) the chage i a object s temperature is proportioal to the differece betwee the temperature of the object at the begiig of the time period ad the room temperature. Thus, if t o is the temperature of the object whe it is placed i a room whose temperature is R, the t, the object s temperature miutes later, is give by the recursio equatio t t = k( t R) Where k is a proportioality costat. a. Suppose that a cup of coffee at 8 C is placed i a room whose temperature is 8 C, ad that mi later the coffee has cooled to C. Fid the proportioality costat k, ad explai the sigificace of its egative sig. b. Show that the recursio equatio give above ca be rewritte as t =.t + 0. c. Usig a calculator, whe will the cup of coffee cool to less tha 7 C?. Medicie. Suppose that i a closed commuity with populatio P, a flu epidemic begis ad that the umber of people ewly exposed to the flu o a give day is proportioal to the umber ot yet exposed o the previous day. a. If f represets the umber of people exposed to the flu days after it begis, explai how the descriptio above leads to the recursio equatio f f = k( P f ), where k is a proportioality costat. b. Suppose i a college commuity of 00 studets, the flue begis with 00 studets exposed to the flu; that is, f 0 = 00. O the ext day, f = 0. Fid the value of k, ad the show that f = f c. Usig a calculator, about how log does it take before the flu spreads through the whole studet body? ANSWERS Practice Set A a =, a =, a =, a = 7, a = 7, a = a. 0,,0, 0. 6 b. d=; arithmetic a. 6,,, b. ot arithmetic 7. Practice Set B ,, , 6,,,0,,.,,,,. 7,0,,6,., 0., 6,., 7.,7,0, ±. ½ Practice Set C. $,0. 600, 6600, 700, 7600.,,,, 7,, $60. m/sec Practice Set D - -

13 = 8. = = Practice Set E. $0 6. $ ,70 Practice Set F. 0. 6, $ Practice Set G.,, 6 or,,6.,,,, or,,,,.,, or,,. 7 th %. % Practice Set H a =, a = , Practice Set J or 0 6a. 6 6b.,,,, 7. A; t = N; t ( ) =. A; t = A;,7. A; 0,. N; 6 6, 7.,,,; G , 0.77, 0.60, 0.60; N 7., 8. 6, 7., 0. 8, ( 7 ). 6. ( )( ) 7. 6( ) 8. = 0 = ( ) = = 0 = = ,8,600. or., 8, ,0 8. 7,00 a. 0 b.,07, o sum ,, 7., 0, m 87. (6 + 8 ) cm. 88 cm. cm a. 8 b. 8 a. 8( ) b. c $ = 6. 0 cm cm 6. $, days p + 8p + 8p + 6p + 70p + 6p + 8p + 8p a + 76a + 60a + 0a + 860a + 6a a + a b + 6a b + a b + b a. a + 0a b+ a b + 0a b 7b. a 0a b+ a b 0a b 0 8 7a. a + a b+ a b + 6a b 7b. x x y+ 0x y 0x y a b 7. 00s t 7. 06a b c d , 0,, t = 80.,,6 - -

14 8. = ( ) s + 80s t + 80s t + 0s t + 0st + t w y Practice Set K 7. x 80xy+ 80xy 0xy+ 0xy y 8. x + x y+ x y + 6 x y +... Practice Set L., 8,.,,.,,. 6, 666, 6., 6, 6.,, 7. 6, 0, ,, 6.,, 6 0., 7,. t = = +. t ( ). t =, t = t +. t = 8; t = t. t =, t = t + 6. t = ; t = t + ( ) 7. t =, t = t + 8. t = ; t = t a.,,,,,,, b. 0a.,8,,, 8,,,8,,... 0b. a. b.,06,7 a. t =.t b. 8 days P = P. S+ = S + +. H = H a. A = 000, A =.0A b. $06,6 a. k =.0 c. after 8 mi b. days - -

15 Sequeces ad Series Arithmetic Sequece:, 8,,,, a a is the first term () d is the commo differece () th The term of a arithmetic sequece is a = a + ( ) d The sum of the first terms of a arithmetic series is ai = a+ a a or i= a + a S = or S = a + ( ) d ( ) - -