2) -12, -112, -212, -312,... Find a 22. 4) 33, 27, 21, 15,... Find a 27

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1 Algebra 2 g a2p0a1_4a gkpuytraj wsvogfqthwhatroef alplqc`._ z YAblMlp irwiwgihvtfsx JrUemsEeFrYvEeKdp. TRF - Sequeces ad Series Name ID: 1 Date Block Determie if the sequece is arithmetic. If it is, fid the commo differece, the term amed i the 1) -40, 160, 360, 560,... Fid a 24 2) -12, -112, -212, -312,... 3) 34, 4, -26, -56,... Fid a 37 4) 33, 27, 21, 15,... Fid a 27 Give the explicit formula for a arithmetic sequece fid the commo differece, the first five terms, ad the term amed i the problem. 5) a = Fid a 26 6) a = Fid a 20 7) a = Fid a 37 8) a = Fid a 20 Give the recursive formula for a arithmetic sequece fid the commo differece, the first five terms, the term amed i the 9) a + 7 = -18 Fid a 34 10) a - 20 = 7 Fid a 24 V H2V0Y1f4y AKUultdaj ps^oefitiw\aqrhef ulvltcq.w T EA\lllw drtipg\h[tmsv krqesswefruvhejdy.r T tmua`dbeg wmift\hy di\uf_i_iihtje[ DAilEgmeNbtrEaA B2_. -1-

2 11) a Fid a 21 12) a + 30 = -4 Fid a 23 Give two terms i a arithmetic sequece fid the commo differece, the term amed i the 13) 2 = -93 ad a 40 = -233 Fid a 26 14) a 20 = 3802 ad a 36 = 7002 Fid a 30 15) 6 = -411 ad a 38 = ) 6 16 ad a 40 = 308 Fid a 29 Give the first term ad the commo differece of a arithmetic sequece fid the term amed i the problem ad the explicit formula. 17) 9, d = -30 Fid a 40 18) = -40, d = 5 19) = -18, d = 6 20) = -3, d 0 Fid a 21 Evaluate the related series of each sequece. 21) 33, 40, 47, 54 22) -8, -14, -20, ) 27, 36, 45, 54 24) -7, -14, -21, -28, -35, -42, -49 z G2P0I1G4V mkquctaay ]SqoifUtNwgaHrWe[ RLVLHCU.i Y XAplplP [rti[gahkttst brtessaewrqv[egdj.i y AMfaNdzeA ywqirtchf YIIOfrir]ixtueq ZAclDgserbFrIar o2a. -2-

3 Evaluate each arithmetic series described. 25) S k 10 5 (12-9k) 26) S (4-10) 6 13 (10k - 8) 27) m S (3m - 10) 28) S k Determie if the sequece is geometric. If it is, fid the commo ratio, the term amed i the 29) 3, 6, 12, 24,... 30) -4, -12, -36, -108,... 31) 1, 9, 25, 49,... 32) 2, 6, 18, 54,... Fid 2 Give the explicit formula for a geometric sequece fid the commo ratio, the first five terms, ad the term amed i the problem. 33) a = ) a = -(-2) ) a = ) a = v T2C0B1U4q AKYujtRav psuodfvtswnaxr[er blmlfcy.a e pailclj VrDimgLhhtKsK drgebste\rxvfebdr.r W smaacdaej EwriKtxhz eiexfrihpiltoe[ AAdlXgeybqrGaP L2f. -3-

4 Give two terms i a geometric sequece fid the commo ratio, the term amed i the 37) a 6 = ad = -3 38) a 2 = 8 ad a 3 = ) a 5 = -162 ad a 6 = ) a 5 = -81 ad a 4 = -27 Evaluate the related series of each sequece. 41) -1, -2, -4, -8, ) 1, 4, 16, 64, ) 1, 4, 16, 64 44) -3, 12, -48, 192 Evaluate each geometric series described. 45) S 10 2 (-3) ) m S 4 3 m ) S -4 (-2) ) S ) , = 9 50) , = 6 51) , = 7 52) , = 7 X T2Q0M1e4e rkyutvas BSeoYfBtxwTaEr[eP QLKLPCk.W B CAvlTlP [rivgchetmsv ^r^eisuewrxvgejdd._ t amfa\duez zwsictghp giamf^i[zi]tgeh DAfl`gBejb\rAau p2e. -4-

5 Algebra 2 R E2B0X1v4I `KTuMtBaM ISlokfotFwFaqrBel ]L]L^C].[ h carlllj RrdisgZhStmsh IrReMs`eJrKvsecdh. TRF - Sequeces ad Series Name ID: 1 Date Block Determie if the sequece is arithmetic. If it is, fid the commo differece, the term amed i the 1) -40, 160, 360, 560,... Fid a 24 Commo Differece: d = 200 a 24 = 4560 = ) 34, 4, -26, -56,... Fid a 37 Commo Differece: d = -30 a 37 = = ) -12, -112, -212, -312,... Commo Differece: d = -100 a 22 = = ) 33, 27, 21, 15,... Fid a 27 Commo Differece: d = -6 a 27 = -123 = 39-6 Give the explicit formula for a arithmetic sequece fid the commo differece, the first five terms, ad the term amed i the problem. 5) a = Fid a 26 Commo Differece: d = 7 First Five Terms: -10, -3, 4, 11, 18 a ) a = Fid a 20 Commo Differece: d = -8 First Five Terms: -40, -48, -56, -64, -72 a 20 = ) a = Fid a 37 Commo Differece: d = 4 First Five Terms: 31, 35, 39, 43, 47 a ) a = Fid a 20 Commo Differece: d = 4 First Five Terms: -3, 1, 5, 9, 13 a 20 = 73 Give the recursive formula for a arithmetic sequece fid the commo differece, the first five terms, the term amed i the 9) a + 7 = -18 Fid a 34 Commo Differece: d = 7 First Five Terms: -18, -11, -4, 3, 10 a 34 = 213 = ) a - 20 = 7 Fid a 24 Commo Differece: d = -20 First Five Terms: 7, -13, -33, -53, -73 a 24 = -453 = v m2c0o1s4x JKAuRttac fswo\fitjwsayrmef RLRLdCP.M A va[l\la WrpiSgAhYtNsl Drfepsle^rCvXeldj.I k SMkaNdNeD FwEiTtXhP GIuEfCiYkiEtjeO ]AXlkgwewbTrGa_ M2e. -1-

6 11) a Fid a 21 Commo Differece: d = -200 First Five Terms: 14, -186, -386, -586, -786 a 21 = = ) a + 30 = -4 Fid a 23 Commo Differece: d = 30 First Five Terms: -4, 26, 56, 86, 116 a 23 = 656 = Give two terms i a arithmetic sequece fid the commo differece, the term amed i the 13) 2 = -93 ad a 40 = -233 Fid a 26 Commo Differece: d = -5 a 26 = -163 = ) a 20 = 3802 ad a 36 = 7002 Fid a 30 Commo Differece: d = 200 a 30 = 5802 = ) 6 = -411 ad a 38 = Commo Differece: d = -30 a 22 = -591 = ) 6 16 ad a 40 = 308 Fid a 29 Commo Differece: d = 8 a 29 = 220 = Give the first term ad the commo differece of a arithmetic sequece fid the term amed i the problem ad the explicit formula. 17) 9, d = -30 Fid a 40 a 40 = = ) = -18, d = 6 a = Evaluate the related series of each sequece. 21) 33, 40, 47, ) 27, 36, 45, ) = -40, d = 5 a 22 = 65 = ) = -3, d 0 Fid a 21 a = ) -8, -14, -20, ) -7, -14, -21, -28, -35, -42, e U2G0i1q4F GKFultEa\ _SFoHf\tmwOaErae ILtLrCu.g e dahl[ll zr]ilgihitfsq Ur`e_sBewrdvOecdg. \ KMDaTdheD ^w[iktghn dighfhiwgit`ey FALlgmeqb`rdaT ]2G. -2-

7 Evaluate each arithmetic series described. 25) S k (12-9k) 6 27) m S (3m - 10) ) S (4-10) 10 28) S k (10k - 8) Determie if the sequece is geometric. If it is, fid the commo ratio, the term amed i the 29) 3, 6, 12, 24,... Commo Ratio: r = 2 1 = 3072 = ) -4, -12, -36, -108,... Commo Ratio: r = 3 1 = = ) 1, 9, 25, 49,... Not geometric 32) 2, 6, 18, 54,... Fid 2 Commo Ratio: r = 3 2 = = Give the explicit formula for a geometric sequece fid the commo ratio, the first five terms, ad the term amed i the problem. 33) a = Commo Ratio: r = 4 First Five Terms: 2, 8, 32, 128, 512 a ) a = -3-1 Commo Ratio: r = 3 First Five Terms: -1, -3, -9, -27, = ) a = -(-2) - 1 Commo Ratio: r = -2 First Five Terms: -1, 2, -4, 8, -16 a 9 = ) a = Commo Ratio: r = 4 First Five Terms: -3, -12, -48, -192, -768 a 9 = x I2F0_1a4i mkyugtdas `S`oSf_tLwraXrGeA NLuLrC_.H F ^Awl`lt CrfiWgehXtEsJ srjecseefrbvtepdr.z b rmha_dwer zw_iatthv fipqfbijcifteel KAXljgGelbCrDai M2D. -3-

8 Give two terms i a geometric sequece fid the commo ratio, the term amed i the 37) a 6 = ad = -3 Commo Ratio: r = 4 a 9 = = ) a 2 = 8 ad a 3 = -16 Commo Ratio: r = -2 1 = = -4 (-2) ) a 5 = -162 ad a 6 = 486 Commo Ratio: r = -3 1 = = -2 (-3) - 1 Evaluate the related series of each sequece. 41) -1, -2, -4, -8, ) 1, 4, 16, Evaluate each geometric series described. 45) S 10 2 (-3) ) a 5 = -81 ad a 4 = -27 Commo Ratio: r = 3 1 = = ) 1, 4, 16, 64, ) -3, 12, -48, ) m S 4 3 m ) S -4 (-2) ) S ) , = ) , = ) , = ) , = g O2F0z1J4w DKMuutSaT dsmosfvtwwpatrdec `LAL[C\.l l DAml[li SrDiMgqh\tOsr `rneysaeyrdv^etdo. x imlaxd[ec ^wai\tfhu ]IvefsiL]iYtzeW CAzlugie`bQrHag m2^. -4-

Unit 6: Sequences and Series

Unit 6: Sequences and Series AMHS Hoors Algebra 2 - Uit 6 Uit 6: Sequeces ad Series 26 Sequeces Defiitio: A sequece is a ordered list of umbers ad is formally defied as a fuctio whose domai is the set of positive itegers. It is commo