is an ordered list of numbers. Each number in a sequence is a term of a sequence. n-1 term

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1 Mthemticl Ptters. Arithmetic Sequeces. Arithmetic Series. To idetify mthemticl ptters foud sequece. To use formul to fid the th term of sequece. To defie, idetify, d pply rithmetic sequeces. To defie rithmetic series d fid their sums. Vocbulry Sequece, term of sequece, explicit formul, recursive formul. Arithmetic sequece, commo differece. Arithmetic series,

2 Wht A sequece: is sequece? is ordered list of umbers. Ech umber i sequece is term of sequece.,,,...,, 3 st term d term - term th term + term A explicit formul describes the th term of sequece usig the umber. It is used to represet terms or fid term. For exmple:,4,6,8,0,.... The th term is twice the vlue of. A recursive formul: formul tht describes the th term of sequece by referrig to precedig terms. For exmple: 33,30,7,4, iitil coditio 3, for

3 Problem : Geertig Sequece usig o Explicit Formul A sequece hs 0 terms of this sequece? explicit formul 3. Wht re the first Aswer:,4,7,0,3,6,9,,5,8. Your tur 3. Wht is the Aswer: 47 term i the sequece?

4 Problem : The umber of blocks i two-dimesiol pyrmid is sequece tht follows recursive formul. Wht is recursive defiitio for the sequece? Aswer Subtrct cosecutive terms to fid out wht hppes from oe term to the ext Cout the umber of blocks i ech pyrmid.,3,6,0, 5, Use to express the reltioship betwee successive terms. To write recursive defiitio, stte the iitil coditio d the recursive formul. d

5 Problem 3: Usig G.C. Usig Formuls to fid terms of sequece. Pierre beg the yer with upid of $300 o his credit crd. Becuse he hd ot red the credit crd greemet, he did ot relize tht the compy chrged.8% iterest ech moth o his upid blce, i dditio to $9 pelty i y moth he might fil to mke miimum pymet. Pierre igored his credit crd bill for 4 cosecutives moths before filly decidig to py off the blce. Wht did he owe fter 4 moths of o pymet? Aswer Step : Write recursive defiitio Iitil coditio: 0 300( use 0 so tht represets R formul :.08 Step : Use clcultor(press MODE key) the blce fter ecursive 9 moth. After 4 moths, Pierre ows 44.36

6 Tke ote: A rithmetic sequece is sequece where the differece betwee y two cosecutives terms is costt. This differece is clled commo differece. A recursive defiitio for this sequece hs two prts: d, for iitil coditio recursive formul A explicit defiitio for this sequece is sigle formul: d for, Exmples of Arithmetic sequeces: 3,6,9,,5, Yes it is A.S. d the differece is 3,4,9,6,5, No, there is ot commo differece

7 Problem 4: Alyzig Arithmetic Sequeces. A. Wht is the 00 th term of the rithmetic sequece tht begis 6,,.? 6,d the commo differece is- 6 5 d Use the explicit formul Substitute d simplify The 00 th term is 50 B. Wht re the secod d third terms of the rithmetic sequece 00,,, 8,.? 00 d the 4 8. There re 3 commo differeces betwee 00 d 8 8=00+3d -8=3d -6=d The commo differece is -6 d the terms re 00,94,88,8,

8 Tke ote: the rithmetic me, or verge of two x y Numbers x d y is. The rithmetic sequece, the middle term of y three cosecutives terms is the rithmetic me of the other two terms. Problem 5: Usig Arithmetic Me Wht is the missig term of the rithmetic sequece.,5,, 59,? Aswer: the missig term is37

9 roblem 6: Usig Explicit Formul for Arithmetic Sequece The umbers of sets i the first 3 rows i sectio of re form rithmetic sequece. Rows d re show i the digrm below. How my sets re i row 3? Row : 6 sets Step : Fid the commo differece d 6 4 Step : Write explicit formul for 3 d Row : 4 sets

10 Wht is series? Tke ote: A SERIES is idicted sum of the terms of sequece. Fiite Sequece: 6, 9,, 5, 8 Fiite Series: (The sum is 60) Ifiite Sequece: 3, 7,, 5,. Ifiite Series: A rithmetic series is series whose terms form rithmetic sequece. Whe series hs fiite umber of terms, you c use formul ivolvig the first d lst term to evlute the sum.

11 ARITHMETIC SERIES S The sum of terms of rithmetic series

12 Problem : Fidig the sum of Fiite Arithmetic Series Wht is the sum of the eve itegers from to 00? Aswer The series is rithmetic with the first term, lst 00 d commo differece d the sum is S Your tur: S Wht is the sum of the fiite rithmetic series ? Aswer 00 4 d 5 d ( )d 4 ( ) ( )d 00 ( ) S 0 0 S

13 Problem : Usig the sum of fiite rithmetic series A compy pys $0,000 bous to slespeople t the ed of the first 50 wks. if they mke 0 sles i their first week, d the improve their sles umbers by two ech week therefter. Oe slesperso qulified for the bous with the miimum possible umber of sles. How my sles did the slesperso mke i the week 50? I ll 50 wks.? Aswer 0 ( 0 d ) d Use the explicit formul to fid the sles i wk. 50 S The slesperso mde 08 sles wk. 50 d 950 sles i ll 50 wks.

14 5 You c use the Greek cpitl letter sigm to idicte sum. You use limits to idicte the lest d gretest vlue of i the series. For exmple you c write the series s Red the sum of s goes from to 5 Tke ote: To write series i summtio ottio you eed explicit formul for the th term d the lower d upper limits. Problem 3: Writig series i Summtio Nottio. Wht is summtio ottio for the series ? Aswer 7 d 4 d = (4 + 3)

15 Problem 4: Fidig the sum of series Wht is the sum of the series writte i summtio ottio. ) Aswer Fid Fid Sice the formul is fuctio the series lier is rithmetic S S , 635 b) 7 There re 70 terms, so

16 Your tur Aswers b) c) - ) 0 ) 40 b) 00 c) 4 Problem 5: Usig G.C. Wht is the sum of the series writte i summtio 70 ottio Aswer 5 3 From the LIST meu. ( d STAT) Your tur 50 Aswer: 4,650

17 Clsswork odd Homework eve