Find the term named in the problem, the explicit formula, and the recursive formula. 1) 5, -15, -35, -55,... Find a 29

Transcription

1 Pre-Calculus A b2k0x1n7t HKVuatlaz ]SPolfdtVwUavrhe_ elvlxcr.i ^ WA]lsle rlisgihotlsu trae^sjeyrevve^d]. Arithetic ad Geoetric Sequeces ad Series Nae ID: 1 Fid the ter aed i the proble, the explicit forula, ad the recursive forula. 1), -1, -, -,... Fid a 2 2) -, -1, - 1, 1,... Fid a 7 Date Period ) -7, -, -41, -4,... Fid a 28 4) , , , - 2 7,... Fid a 1 Give the explicit forula for a arithetic sequece fid the coo differece, the ter aed i the proble, ad the recursive forula. ) a = Fid a 6 6) a = -1 - Fid a 40 7) a = + 7 Fid a 7 8) a = Fid a 2 Give the recursive forula for a arithetic sequece fid the coo differece, the ter aed i the proble, ad the explicit forula. ) a - 10 = 27 Fid a 28 10) a + 20 = Fid a J g2m0u1e7n YKpuBtoab [S\oAfDt]wZaereY LzLGCV.v t pauldlp Irpi`gkhRtEsK BrkewsreurcvxeVdf.e r AMcaXdke \waiftshx NILAftiYviQtEeK \AClWghezbhrqao l2l. -1-

2 11) a Fid a 22 12) a = -18 Fid a 7 Give two ters i a arithetic sequece fid the coo differece, the explicit forula, ad the recursive forula. 1) 2 = -08 ad a 2 = ) = -81 ad a 6 = ) = 87 ad a 4 = 7 16) 4 = 47 ad a 6 1 Evaluate each arithetic series described. 17) S i 2 (2i - ) 18) S (10-12) 1) S (2-1) 20) S (4-6) 40 Deterie the uber of ters i each arithetic series. 21) S (k - 10) = 0 22) k S (1-10k) = k 2) S i i 62 24) S (7-2) = R f2f0r1g7y MKaurtHah QSKoOfMtwUaFrYej [LILlCM.B d wawl]la Wrji]gQhEtJsu GraeosCeNrXvqeIdF.w K jmyasdueh swkigtvhh aiddfyiydietoec laylrgwevbrrpa` o2d. -2-

3 Fid the coo ratio, the ter aed i the proble, the explicit forula, ad the recursive forula. 2) -2, -10, -0, -20,... Fid a 26), 12, 48, 12,... Fid a 27) 2, 8, 2, 128,... Fid 0 28), 6, 12, 24,... Fid 1 Give the explicit forula for a geoetric sequece fid the coo ratio, the ter aed i the proble, ad the recursive forula. 2) a = - 1 Fid a 0) a = -4-1 Fid a 1) a = (-2) - 1 Fid 1 2) a = Fid 0 Give the recursive forula for a geoetric sequece fid the coo ratio, the ter aed i the proble, ad the explicit forula. ) a = -1 Fid 1 4) a Fid 1 C D2G0Z1F7b akkuetlax cslorfxtgwtacrxeo FLWLHCg. I taflilt briimg\hfthsp drcerszeqr_vjekdv.i F UMfawdJe _wmittnhw LIIHfviTEitAew earlogqebbyrva p2n. --

4 ) a 4 = 0. Fid 0 6) a 2 = -2 Fid 2 Give two ters i a geoetric sequece fid the coo ratio, the ter aed i the proble, the explicit forula, ad the recursive forula. 7) a 2 2 ad a = -768 Fid a 8) a 6 = Fid a 2 24 ad a = ) a 62 ad a 2 = 6 Fid 1 40) a = -24 ad a 2 = 48 Fid a Evaluate each geoetric series described. 41) S 2 i ) i S ( 1-1 i 2)i 8 4) S ( k )k 8 44) S -4-1 Deterie the uber of ters i each geoetric series. 4) S ( = 46) ) 24 S ( - 1 4) 41 - = 12 47) S 0.8 k - 1 = ) k S - (-) i - 1 = 12 i O V2v0A1\7F MKwueteai \SYoZfLtywVaCrEew ULLvCd.i k waplxlc vrziwgzhrtesi crzeiscerkvqeada.n c VM[akdqeJ wwhitthhd ZINwfsiEVipt]eG qawl^ggebbrsag h2x. -4-

5 Pre-Calculus E C20f1[7E XKiuNtCao osqoqfjtwpahried xl\lics.n \ KALlxli aryiugkhwtdsn zrsehsneirtvyerd^. Arithetic ad Geoetric Sequeces ad Series Nae ID: 1 Fid the ter aed i the proble, the explicit forula, ad the recursive forula. 1), -1, -, -,... Fid a 2 a 2 = - = = ) -7, -, -41, -4,... Fid a 28 a 28 = -1 = = -7 Date Period 2) -, -1, - 1, 1,... a = 67 7 Fid a 7 = = - 4) , , , - 2 7,... a = Fid a 1 = = Give the explicit forula for a arithetic sequece fid the coo differece, the ter aed i the proble, ad the recursive forula. ) a = Fid a 6 Coo Differece: d = 2 a 6 = = -18 7) a = + 7 Coo Differece: d = 7 Fid a a 7 7 = ) a = -1 - Coo Differece: d = - Fid a a = = -20 8) a = Coo Differece: d = -200 Fid a a 2 2 = = Give the recursive forula for a arithetic sequece fid the coo differece, the ter aed i the proble, ad the explicit forula. ) a - 10 = 27 Fid a 28 Coo Differece: d = -10 a 28 = -24 = ) a + 20 = Fid a k V2s0^1E7l KxuDt]aK LSfo[fNtfwFayrPeh [LpL[Cb.D ^ tavlxle Xrji\guhMtsN VryeKsHe^rTvjeeda.j d tmyaldheb bwpigtshk LIKkfdiWoictNed caclggejbtrlar D2N. -1- Coo Differece: d = 20 a =

6 11) a Fid a 22 Coo Differece: d = -6 a 22 = -112 = ) a = -18 Fid a 7 Coo Differece: d = -100 a 7 = -618 = Give two ters i a arithetic sequece fid the coo differece, the explicit forula, ad the recursive forula. 1) 2 = -08 ad a 2 = -08 Coo Differece: d = -0 = = 22 14) = -81 ad a 6 = -681 Coo Differece: d = ) = 87 ad a 4 = 7 Coo Differece: d = 0 = = - 16) 4 = 47 ad a 6 1 Coo Differece: d = = + + = 8 Evaluate each arithetic series described. 17) S i 2 1) S 2 2 (2i - ) (2-1) 18) S (10-12) ) S 040 Deterie the uber of ters i each arithetic series. (4-6) 21) S (k - 10) = 0 k 1 22) S (1-10k) = k 20 2) S i 2 i 62 24) S (7-2) = X2U0F1`7U pkvurtkav [SUo\fCtYwtazrfeP wlglfc.\ E gadlulp ]r]i]gkhjtsj wrke[sbelravfeldp.d F EMRa^dIeT Cw^iMtyhi VIETfBidgiAthez jaolgkegbsr_ao t2w. -2-

7 Fid the coo ratio, the ter aed i the proble, the explicit forula, ad the recursive forula. 2) -2, -10, -0, -20,... Fid a Coo Ratio: r = a = = -2-1 = -2 26), 12, 48, 12,... Fid a Coo Ratio: r = 4 a 6608 = = 27) 2, 8, 2, 128,... Fid 0 Coo Ratio: r = 4 0 = = = 2 28), 6, 12, 24,... Fid 1 Coo Ratio: r = 2 1 = 072 = = Give the explicit forula for a geoetric sequece fid the coo ratio, the ter aed i the proble, ad the recursive forula. 2) a = - 1 Fid a Coo Ratio: r = a 68 = 0) a = -4-1 Coo Ratio: r = Fid a a = = -4 1) a = (-2) - 1 Fid 1 Coo Ratio: r = -2 1 = 072 = 2) a = Coo Ratio: r = Fid a a = 062 = 0.2 Give the recursive forula for a geoetric sequece fid the coo ratio, the ter aed i the proble, ad the explicit forula. ) a = -1 Fid 1 Coo Ratio: r = -2 1 = = -(-2) - 1 4) a Fid 1 Coo Ratio: r = = (-2) - 1 r R2P0h1k7Z BKpuXtGai hsfolfftwdawrreb ulwl`ch._ E aaolgly LrFiugChCt_s vrwesaeirevieidt. t omwatdleq woi[tmhf viznf]ibeitttei xaslogtefbxrma Z2j. --

8 ) a 4 = 0. Fid 0 Coo Ratio: r = = ) a 2 = -2 Fid 2 Coo Ratio: r = 2 2 = -406 = Give two ters i a geoetric sequece fid the coo ratio, the ter aed i the proble, the explicit forula, ad the recursive forula. 7) a 2 2 ad a = -768 Coo Ratio: r = -4 Fid a a = = - (-4) = - 2 8) a 6 = 24 ad a = Coo Ratio: r = - 81 Fid a a = ( = ) ) a 62 ad a 2 = 6 Coo Ratio: r = Fid a a = 2-1 = 2 Evaluate each geoetric series described. 41) S 2 i - 1 i ) S ( k )k = a ) a = -24 ad a 2 = 48 Coo Ratio: r = - 1 = -2 2 Fid a a = - 8 ( = ) 7 42) S ( 1-1 i 2)i ) S = -6 Deterie the uber of ters i each geoetric series. 4) S ( = 46) ) 24 S 6 4 ( - 1 4) 41 - = 12 47) S 0.8 k - 1 = k 48) S - (-) i - 1 = 12 i 4 a \2y0J1M7M `KugtJat ysqotfvt^wra_req ]LjLhCF.N L faflklk zraijglhmt_sa prvegspeqrovyeyde.x M VMcaBdPej ZwiTtXhB DIkbfXicUijtieb yaslggeevb^ruaf T2O. -4-