Arithmetic: Calculators Permitted S = 11(01 + a,, ) " 2 0n= 1. Find 0 25 for the sequence of positive 3-digit numbers thataremultiples of7. los 118 IIQ).., J ) O:z.s:: 105+21(1) ['lljj ame, _ Dat e. No _ Geometric: (. (1- r " ).J = a ~~. " 1 (1- r ) 1. Find a 22 fo r the sequence of positive 3-digit numbers that are multiples of 8. 2. How many te rms are in the sequence: - 5,4, ]3, 22,...,121? 2. How many terms are in the sequence: -6,- ]4, - 22,..., -422? \ ~I = -S ( -::. -14 \3~ = ~f\ 25 1/ 2 3. Find t he sum of In-] 3. Find the sum of I 3n + 2 n=1 no l <S> 4. Find t he sum of 2) Cty-1 4. Find t he sum of I: n= l n=1 v: 4<+)"-1 5. In the arithmetic seq uence, if 0 3 = 3 and 0 12 = 12, 5. In the arit hmetic sequence, if a 3 = 8 and a 7 = 20 I find 03-l find 0 50 lj:::o l t- lld 3=Q, ~ q~ d I =: d - - - - - - - - - -
6. In a geometric sequence, if a 3 =8 and a 6 =64, 6. In a geomet ric sequence, if ~ =36 and a 6 =972, find alo lo4 = Q,.r5 : find all B= Ut ' rlj. D= 7. Find the fourth term (simplified) of (x 2 _ y )8 7. Find t he fourth term (simplified) of (x 2-2y)12 8. Write in sigma notation: 1+ 3+ 5+...+ 99 qq =\+ -1)0 ClC\ ~ - \ =- Vl 5 6 L n.::- I dn -I 1 8. Write in sigma notation: 4+ 8+ 12 +...+ 312 9. Find three positive geometric means between 2 and 162. 2, _--J _ -, _ --J' 162 0, 0.5 ILPd=~' r 4 ~ \ =r 4 [ tv )IB,5Y J =r 10. Find the sum of the 2-dlgit multiples of 4. \0+ \\0+ do ~ qlo : \(} -\- ( - \)~ to -- L\ 5 5'20;:: ~(\ d- LP") ffi -= 4 1 d~ :: Y\ [UOOJ 9. Find three positive geomet ric means between 2 and c:?5'1d 2, _ --, _ --, _ ---', 2592 10. Find t he sum of the 3-digit multiples of 5.
11. Find th e sum of 5+ 1+t+ ~15 +... - 5 =(15 \ 1-'tS LD 11. Find th e sum of 4+ 3+++... 12. Find 8 40 (the sum of th e firsttot erms) fo r 57 + 55 + 53 +... ~(-~) ~= ~ O(Sl+(-d-\')).-----.d (l do] 13. Find x so th at 9x, x, x - 8 is an arit hmetic sequence. >\ - OJ,,, = X--fJ-X ~ " ~X -= {Tj 12. Find 8~ 5 (t he sum of the first 55 terms) fo r 37 + 33+ 29 +... 13. Find x so that 9x,x,x - 8 is an arit hmet ic sequence. 14. A class ic car appreciates in value 3% each year. The original value is $20,000 at th e beginning of the first year. Find the value at t he end of 25 years. ~~ d 0 (\.a~)~s 14. A value of a rare coin increases one-tenth each year. If the coin is worth $30 now, how much will it be wort h in seventeen years? L11>4-l6 l5. ~ J 15. Some bricks are stacked so that there are 6 bricks in the top row and 3 more bricks in each successive row down to the ground. If there are 35 rows in all, how many bricks are there in the whole stack? 035 = lo T ~L\(~ I =-\()1; 15. The seats in the new amphitheater are arranged like an open fan. The first row seats 26 people and the second row seats four more, and the next row fo ur more, etc. If there are 30 rows altogether, how many seats does the amphitheater have?
16A. Find the third, fourth, and fifth terms of the sequence: II = 2, 1 2 = 5, I" = 2/"_2+ 1"_1 16B. Find the third, fourth and fifth terms of the sequence: I. = 3, I" = 1"_1 + 3n 17A. Give a recursive definition for the sequence: 1, 5, 9, 13,...,::: \) 17B. Give a recursive definition for the sequence: 243, -81, 27, -9,... 18A. The population of a country increases each year by 3%. Additionally, 10,000 people move out of the country each year. Give a recursion equation for p" the population in n years. If the current populat ion if $2,500,000, what will t he population be in 5 years? 18B. Mr. Brown invests money into an account that pays 2% annual interest. Each year he adds $1000 to the account. Write a recursion equatio n for An th e amount of money in the ccount in n years. If he starts the account with $3,500, how much will he have after 6 years? /'1 A. Prove 2 + 4 + 6 +...+ 2n j n 2 + n tv n e N G) S"oW +r \)J... TCr n - I " ~-+ L\- ~l.: \~ \ v 'i d+4 -tlp +... srovj+ Lo+.. +.2(1l- ) + "Or -, Q ( I(-\J ~ C~-l)"1.-+(jL_ () M.B. Prove 2+5+8+...+(3n-l)= n(3n+l) 'VnEN 2 ::: k~ '2:iG * \«+ ~ ={l 'J.-t kj\j "a. + ::r r 7 TMA equences and SeriesPractice Test.14
21B. Prove (n 3 + 3n 2 + 2n) is divisible by 3 ":In E N 22A. Prove (18 11 - I) is divisible by 17 ":In E 22B. Prove (12 11-1) is divisible by 11 ":In E N (D 5h:w i fu.l for :. I ( tel- I -7 \1 v t 66 or n= ( I IB ~t-1 ~ = - I ~ '@- I 1. rb etc.- \ 1- :J \ \ ~ \1 -:-\1 ty& P 2.... (\t)y1_ l 'r:- \l \J n-e f\:i MAScqu nces and SeriesPractice Tcst.14
Arit hmetic: Calculators Permitted - Nam e~ _ Date"- No _ ; Geometric: s = J/(or +0,,) l l ' (1 -,." ) a = a r n -,J = 0 - -.\ ; =-,II a l r n I " " I (1-,.) 1-,. r <1 1. Find a 25 forthe sequence of positive 3-digit numbers that are multiples of 7. 1. Find a 22 for the sequence of positive 3-digit numbers that are multiples of 8. I 't I 11'4 J " 0 2.~ C1.'L1--:=' (OY- + (21- IJ<0 ~ 1 ~l d-j 2. How many terms are in th e sequence: - 5, 4 13, 22,...,121? 25 3. Find the sum of Ln-1 n~ l 2. How many terms are in the sequence:. -6, - 14, - 22,.." -422? - 4d ~ = - lo+cn- f')(-6') -4d-d = ~ -~n n=5~ 112 3. Find th e sum of I 3n + 2 n- I 5 11 1 = 112(S + Qol,) 2.. 00 4. Find the sum of I7ctr-1 n ; [ 00 4. Find the sum of L 4(+)"-1 11=1 5. In the arit hmetic sequence, if a 3 =3 and a l 2 =12, fi nd a 34 S. In th e arit hmetic sequence, if a 3 =8 and a 7 =20 r find a so (. ---- - ------- - -------- -
6. In a geometric sequence, if a 3 =8 and a 6 = 64, fin d a lo 7. Find the fourth term (simplified) of (x 2 _ y )8 6. In a geometric sequence, if a 3 =36 and a 6 =972, find a l l C\ld.-=Q \.r '5 s ~=o. l r1: ' Ctll :.: 4(3'0') [ J31o \GHo \ 7. Find the fourth term (simplified) of (x 2-2yy2 8. Write in sigma notation: 1+ 3 + 5+...+ 99 8. Write in sigma notation: 4 + 8 + 12 +...+ 3 12 0\2 :::: 4 +(n- I'fJ_----. 312 =4n r«1b l5~n L 4n 9. Find three positive geometric means between 2 9. Find three positive geomet ric means between 2 and and 162. ~. '2sct 'L.,_--, 162 2, 0-, 2.Sg2= 2 r 4 \2L1LP::. r~ y- = lo,_--, 2592 0.5 10. Find th e sum of the 2-digit multiples of 4. 10. Find the sum of t he 3-digit mult iples of 5. 100+\05;-\\0+. \' +CfCJ5 qti5 -loot(n-i)s ~~;grj SU'JQ = 1f30(llXltO{1SJ r--- --,. 2. IQtJ5501 I - ------- -
,------------------------r--------------.-----.- --,-- 11. Find the sum of 4 + 3 +t+.. 11. Find the sum of 5+1 + ++-!5 +. 4 -~ 12. Find 8 40 (the sum of the first terms) for 57 + 55+ 53+... 12. Find 8 55 (the sum of the first 55 terms) for 37 + 33 + 29+... I 13. Find x so th at 9x, x, x- 8 is an arit hmetic sequence. [ -:11 5 J 13. Find x so that 9x, x, x 8 is an arit hmet ic sequence. x-clx= X-B-X -8X=: -6 xffi 14. A classic car appreciates in value 3% each year. The original value is $20,000 at t he beginnin g of t he first year. Find th e value at the end of 25 years. 14. A value of a rare coin increases one-te nt h each year. If the coin is worth $30 now, how much will it be wort h in seventeen years? te;= X)(!.I)11 [ II> \5 \. (03) 15. Some bricks are st acked so that there are 6 bri cks in the top row and 3 more bricks in each successive row down t o t he ground. If there are 35 rows in all, how many bricks are there in the w hole stack? 15. The seats in the new amphit heater are arra nged like an open fan. The first row seats 26 people and the second row seats fo ur more, and the next row four more, etc. If th ere are 30 rows alt oget her, how many seats does t he amp hit heat er have? 0.20= 1l.o +2q(Ll ') -= \4d..
16A. Find the third, fourth, and fifth terms of the sequence: II = 2, 1 2 = 5, In = 21"_2+ ' ''_1 16B. Find the third, fourth and fifth terms of the sequence: II = 3, I" = 1"_1 + 3n 17A. Give a recursive definition for the sequence: 17B. Give a recursive definition for the sequence : 1, 5, 9, 13... 243, -81, 27, -9,... - -1 -I 18A. The population of a country increases each year by 3%. Additionally, 10,000 people move out of the country each year. Give a recursion equation for p" the population in n years. Ifthe current population if $2,500,000, what will the population be in 5 years? 18B. Mr. Brown invests money into an account that pays 2% annual interest. Each year he adds $1000 to the account. Write a recursion equation for A" the amount of money in the account in n years. If he starts th e account with $3,500, how much will he have after 6 years? - :)500 An ::. I.Od An-I t I 'Vl lo ljrs, Al:: D 1..., '-'~ ~A. Prove 2 +4+6+...+2n =n' +n "v'n E N I '1. n(3n+l) B. Prove 2+5+8+...+(3n-l) = "v'nen 2 ShDuJ -ty"\,u.. foy n=- I ( 30) - \ ") ==, ( ~{) \)./ 1 trw.. for n=k-,.2 +::>+15+...+ (~ ( t-i) -I j == (~ -I X?1/l- i)+ll 2 ~ 1tUL fer n= ~ + "+ B +- " +( ~~ -IJ-I It ~ - I -=- L~ - \'i3~1) -t 3~ 1 1. = 3 ~-51(-t 2 + 19fd::.. 'L -=?t-1-+ ~ ~ = K(?j. 'L TMA Sequences and Series Practice TesLl4
5"+ 1 _5 -- '11I1 E N 4 21A. Prove (n 3 + Sn) is divisible by 3 Vn E N 218. Prove (n 3 + 3n 2 + 2n) is divisible by 3 "In E N I 5faA) -trw -for - I ( I~+ I U I ~ ).!:- 0 v' 2. /-'f:6l,t ml -trw for'" h = IC ( k?+ ~ll!"+ ~ J ~ 3 3 ry:u.>"tylat fc'i - t< I ( k- H)~ + ~(\(:+ I )~+ 'J.( ~~+:> 2..-+~ + l +::JK.~+ lp K.+ 3 T L d- - - t(~+~~~ CT ;+- qk-t- LD +-:>ls ~ -:~ ty '2.. L -:- 3.", Cn 3 + 3n'l-+ ~ )-7 ~ V n E 22A. Prove (IS n - I) is divisible by 17 Vn E N 22B. Prove (12 n - 1) is divisible by 11 Vn E N, srow -w-w -{Of n= I ( l;}1-, ) -7 u./ :-tv\)" ' ior -= ~ ( \ ~ l<-_ \ J7 II 3 W tyu.l fey :: 1'.+ ( 1~1 1_ \ ~\.@-l \I~ -t ~~- \ c:- --1 ''-_-:--_'"':''' -7- \ I ~ \,. 1 - I. I TMASequences and Series PracticeTest.l-t