Honors Algebra 2 Name___________________________________ Sequences and Series Date________________ Period____ ©5 Z2K031z1 u FK5u1tQa2 cScocfUtnwIa5rveC sLxLKCm.5 o HAfl5lP sr1ingYhstBsb rrJersOeIrdvHeMdq.R Determine if the sequence is arithmetic. If it is, find the common difference, the 52nd term, the term named in the problem, and the explicit formula. 1) 1, 9, 25, 49, ... Find a30 2) 2, 4, 12, 48, ... Find a26 Given the explicit formula for an arithmetic sequence find the common difference, the 52nd term, and the term named in the problem. 3) an = 36 + (n − 1) ⋅ 20 4) an = 12 + (n − 1) ⋅ −10 Find a28 Find a27 Given two terms in an arithmetic sequence find the common difference, the 52nd term, and the term named in the problem. 5) a11 = 35 and a39 = 203 6) a11 = −81 and a31 = −241 Find a28 Find a39 Given the first term and the common difference of an arithmetic sequence find the 52nd term and the term named in the problem. 7) a1 = −6, d = 7 8) a1 = 19, d = −30 Find a40 Find a39 Given a term in an arithmetic sequence and the common difference find the 52nd term and the term named in the problem. 9) a26 = 4982, d = 200 10) a35 = 177, d = 5 Find a34 ©M U260S1H1Y rKmugtHa0 jSlo2f5tHw0azrmeq 6LlLdCy.Y g lAxlclm OrliFgph0t1sx OrHeUs4eorGvperdK.N 1 sMna2dgej kwcimtMha eIpnGfBiwnHiQtter YA1lQgDe3bMrmaa E2c.Z Find a30 -1- Worksheet by Kuta Software LLC Find the missing term or terms in each arithmetic sequence. 11) ..., −15, ___, ___, ___, ___, ___, −75, ... 12) ..., −32, ___, ___, ___, ___, 13, ... 13) ..., 30, ___, ___, ___, 22, ... Find the missing term or terms in each geometric sequence. 14) ..., 2, ___, ___, ___, ___, ___, 128, ... 15) ..., 4, ___, ___, ___, 64, ... 16) ..., −4, ___, ___, ___, ___, −972, ... Evaluate the related series of each sequence. 17) 25, 32, 39, 46, 53, 60, 67 18) 22, 26, 30, 34 Evaluate each arithmetic series described. 15 19) 21) Σ (8m − 7) 7 20) Σ (7i − 4) m=1 i=1 35 50 Σ (15 − 9i) 22) i=1 23) a1 = 5, an = 19, n = 8 ©I k2M0y1e12 zKguftsai mSDoTfdtWwGaFrBeR PL0LuCz.Q K wAolqlm 8r1iOgThMt8s7 TrreDs3eMrpvteZdm.D m wM2afdUev pwviGtphE ZITn3fAiqnPivt5ek wAsl9gwekbsr5a6 Y27.6 Σ (5 − 9n) n=1 24) a1 = 10, d = 4, n = 6 -2- Worksheet by Kuta Software LLC 25) a1 = 17, d = 4, n = 20 26) (−1) + 8 + 17 + 26..., n = 8 Determine the number of terms n in each arithmetic series. 27) a1 = 8, an = 50, S n = 435 28) a1 = 23, an = 137, S n = 1600 Determine if the sequence is geometric. If it is, find the common ratio, the 8th term, and the explicit formula. 29) −3, 12, −48, 192, ... 30) −4, 16, −64, 256, ... Given the explicit formula for a geometric sequence find the common ratio and the 8th term. 31) an = −4 ⋅ (−2) n−1 32) an = 2 ⋅ (−6) n−1 Given two terms in a geometric sequence find the common ratio and the 8th term. 33) a3 = 16 and a4 = 32 34) a3 = 16 and a4 = −32 Given the first term and the common ratio of a geometric sequence find the 8th term. 35) a1 = −2, r = 3 36) a1 = −2, r = 4 Given the second term and the common ratio of a geometric sequence find the 8th term and the term named in the problem. 37) a2 = −6, r = −2 38) a2 = 6, r = 2 Find a9 ©o n2G0E141f KKFuRt2ar SSGogfBtvwlaarNew vLhLjCF.J M gAylzl0 gr0ilgAhXtJsZ MryemsZe2rgvmemdK.u r 0MSahdxey zwDidt XhR ZIVnefoiznSiktzeh 6AGlygReSbMr1aY E28.g Find a10 -3- Worksheet by Kuta Software LLC Given a term in a geometric sequence and the common ratio find the 8th term and the term named in the problem. 39) a2 = 3, r = −3 40) a4 = 27, r = 3 Find a9 Find a12 Given two terms in a geometric sequence find the 8th term and the term named in the problem. 41) a5 = −16 and a1 = −1 42) a1 = 3 and a3 = 12 Find a10 Find a12 Evaluate each geometric series described. 43) 2 + 10 + 50 + 250..., n = 9 10 44) Σ4 n−1 n=1 7 45) Σ 2 ⋅ 5k − 1 46) a1 = −3, an = −6561, r = 3 k=1 47) a1 = −1, a8 = −16384, r = 4 48) −2 − 8 − 32 − 128..., n = 9 Determine the number of terms n in each geometric series. 49) a1 = −2, r = 3, S n = −26 ©2 A200d1d1s AKmuPtla9 WSboXfgt aw0a greeP LL9L6Cn.r W GAllIlh irXiXgphutYsZ drqeMszesrfvieCdC.a z 1M5apdlez PwtibtuhC FIKnhfviqnaiRt Me5 OAFlPg9eDbxrgaG b2b.i 50) a1 = −2, r = 3, S n = −728 -4- Worksheet by Kuta Software LLC Answers to Sequences and Series 1) Not arithmetic 2) Not arithmetic 3) Common Difference: d = 20 a52 = 1056 a28 = 576 4) Common Difference: d = −10 a52 = −498 a27 = −248 5) Common Difference: d = 6 a52 = 281 a28 = 137 7) a52 = 351 8) a52 = −1511 a40 = 267 a39 = −1121 11) 14) 17) 21) 25) 29) −25, −35, −45, −55, −65 4, 8, 16, 32, 64 15) 322 18) −5145 22) 1100 26) Common Ratio: r = −4 a8 = 49152 35) a8 = −4374 a39 = −305 9) a52 = 10182 a34 = 6582 a9 = −6561 43) 976562 47) −21845 a30 = 152 Explicit: an = −4 ⋅ (−4) n − 1 33) Common Ratio: r = 2 a8 = 512 36) a8 = −32768 37) a8 = −384 a9 = 768 39) a8 = 2187 10) a52 = 262 12) −23, −14, −5, 4 13) 28, 26, 24 8, 16, 32 16) −12, −36, −108, −324 112 19) 855 20) 168 −11225 23) 96 24) 120 244 27) 15 28) 20 30) Common Ratio: r = −4 31) Common Ratio: r = −2 a8 = 65536 a8 = 512 Explicit: an = −3 ⋅ (−4) n − 1 32) Common Ratio: r = −6 a8 = −559872 6) Common Difference: d = −8 a52 = −409 40) a8 = 2187 41) a8 = 128 a12 = 177147 44) 349525 48) −174762 ©7 y2o0B1j1w BKeugtGaA iSboZfFt 2wWaVrIej sLoLTC S.F X gAklslL orAiagLhNtRsN KrleWsIeLrdvbecdI.t H VMuaUdveN Pw1iwt3hw BIwn5ffiUnAixtxeO NAmllgreGbmruaJ P2J.3 a10 = 512 45) 39062 49) 3 -5- 34) Common Ratio: r = −2 a8 = −512 38) a8 = 384 a10 = 1536 42) a8 = 384 a12 = 6144 46) −9840 50) 6 Worksheet by Kuta Software LLC