UNIT #5 SEQUENCES AND SERIES COMMON CORE ALGEBRA II

Transcription

1 Awer Key Nme: Dte: UNIT # SEQUENCES AND SERIES COMMON CORE ALGEBRA II Prt I Quetio. For equece defied by f? () () f d f f, which of the followig i the vlue of f f f f f f (). I the viul ptter below, the umber of qure i ech ptter form equece. Which of the followig four equece defiitio properly model the umber of qure,? I. II. III. d IV. d () I d III () II d IV II d III I d IV. Which of the followig formul properly decribe the equece, 0,, d 6 Clerly. A well, we c tet the formul give i I d II to ee tht, 0, etc.,,,,... 8 () (), 0, 8. If equece i defied by c d c the wht i the vlue of the 0 th term of thi equece? c () 80 () Sice the me mout i beig dded ech time to geerte the ext term of thi equece, it i d, o: rithmetic. Recll tht c emathinstruction, RED HOOK, NY, 0

2 . A cocert hll i cotructed o tht ech row h more et th the row i frot of it. If the firt row coti et, how my et doe the 0 th row coti? () () Sice the me umber of et i beig dded ech time to geerte the ext row thi crete d, rithmetic equece. Recll tht o: r If the firt three term of geometric equece re 8,, d x, the wht i the vlue of x? () () 8 I geometric equece, the rtio of coecutive term i cott. Thu, we c crete the equtio: x 8 6x 6x 6 x. The umber of cube i ech ptter below form geometric equece. How my cube would be i the 0th ptter? () 6,6 9,68 () 9,09, I geometric equece, the followig i true: r Sice d r we c coclude: ,68 8. Which of the followig i the vlue of i? i () () () emathinstruction, RED HOOK, NY, 0

3 9. For y vlue of x, the um x i equivlet to 0 () 6x () x 6 8x 6x 0xxxx x0 6x x 6 () 0. The erie c be repreeted by () () The um of the firt 00 poitive, eve iteger i (),00 (),00 0,00, ,00. Wht i the vlue of rithmetic erie whoe firt term i 00, whoe commo differece i 8, d which h 0 term? () 0 () If the followig um repreet geometric erie, the which of the followig i it vlue? (),60 (),600 98,,60 6, log log 0 0, 60 emathinstruction, RED HOOK, NY, 0

4 . I term of, wht i the vlue of 6 r r if 0 r? () () r r r r r r r r r r r r 6 r r (). A mortgge h iitil blce of $0,000 d i chrged % yerly iteret pplied mothly. If pero me pymet of $000 ech moth, which of the followig i cloet to the mortgge blce fter moth of pymet? After oe moth: () $,6 () $8,60.0 0, 000, 000 9, 6 $,0 $8,80 After moth:.0 9, 6, 000 9, 8. After moth:.0 9, 8., 000 8, 80. Free Repoe Quetio 6. A equece i give by the recurive defiitio: d Stte the fourth term of thi equece. Show how you rrived t your wer.. Write the followig i implet form i term of x. ( ix i) i x i i , 8 x x 6x 8 x x x 9x 8x 9 9x x 8 9 x emathinstruction, RED HOOK, NY, 0

5 8. For ome vlue of x the equece x, x,x form the firt three term of rithmetic equece. () Fid the vlue of x. (b) Determie the umericl vlue of the th term of thi equece. xxxx x0 x6 x 6 x x x 9 x x x x d (c) Fid the um of the firt 0 term of thi equece. Show your lyi , I geometric equece, the firt term i 8 d the eighth term i,96. Determie the ecod term of thi equece. Show how you rrived t your reult. 8r,96 8 8,96 r 8 8 r r 8 r 8 0. If equece i defied by the recurive formul: c 00 d c c the wht i the vlue of 0 c. Show how you rrived t your wer. Sice ech term i cott multiple of the previou term, thi i geometric equece, which give rie to geometric erie. The um of which i give by the formul: r r emathinstruction, RED HOOK, NY, 0

6 . A lie egmet i broe ito five ectio tht form geometric equece. The mllet ectio i 6 iche d the lrget ectio i 8 iche. () Wht i the commo rtio betwee the five ectio? Show how you rrived t your wer. 6 8 r 8 6r 8 r 6 8 r 6. (b) Wht i it overll legth of the lie egmet? Expli your pproch OR r r 6... A erie, S, i give by the formul S i x. i0 () Write polyomil expreio for S. (b) Write polyomil expreio for x S. x x x x 0 x x x x x x x x x x x x (c) Uig your wer from () d (b), write expreio for x S S i implet form. x x x x x x x x x x x x x x x x (d) Expli why, for x, S x x x x x x x x.. Roie i fillig hot tub with wter i uch wy tht he origilly dd 0 gllo, the 0 gllo, the gllo, etceter, with ech mout beig 80% of the previou mout dded. How my time mut he fill the hot tub before the totl mout of wter i greter th 00 gllo? Oly lgebric pproch will be ccepted log.8 log. log. log.8 log.8 log.. emathinstruction, RED HOOK, NY, 0 Sice we cot fill the bthtub frctiol umber of time, we mut fill it t let 8 time before the totl mout dded will be greter th 00 gllo.

7 . I mortgge, the mothly pymet, m, i clculted uig the formul: P r m where P i the pricipl of the lo, i the umber of pymet, d r i the mothly mortgge rte, expreed deciml. () If lo hd pricipl mout of P $0,000 d yerly rte of %, wht mothly pymet would be eeded to py off the lo i exctly 0 yer? Show how you rrived t your wer. r.0 r ,000 m $, (b) If the pricipl w till $0,000, but the yerly rte w 6%, determie lgebriclly the umber of yer it would te to py off the lo with mothly pymet of $,000. Show your wor. Roud to the eret teth of yer..06 0, log.00 log 0. log0. log.00 log.00 log moth 9 6. yer emathinstruction, RED HOOK, NY, 0