7.3 Sequences - Applications - Worksheet 1 [Questions + Answers]

ID: 1 Secondary I Name___________________________________ 4.3 Arithmetic and Geometric Sequences Worksheet Period____ ©6 227091x3k eKouptMaj GSSoqfetUwLavrVej TL9LKCp.W l WA5lKlm qroiXgOhHtks6 ZrTehsceTrgvSebdE.w Determine if the sequence is arithmetic. If it is, find the common difference. 1) −9, −109, −209, −309, ... 2) 28, 18, 8, −2, ... 3) 28, 26, 24, 22, ... 4) −16, −6, 4, 14, ... 5) −8, −4, 0, 4, ... 6) 1, 1 1 , 0, − , ... 2 2 Find the common difference and the three terms in the sequence after the last one given. 7) −39, −33, −27, −21, ... 9) 17, 13, 9, 5, ... 8) −27, −17, −7, 3, ... 10) 1 23 43 21 , , , , ... 5 15 15 5 Find the common difference and the recursive formula. 11) 9, 19, 29, 39, ... 12) 22, 19, 16, 13, ... 13) −3, 97, 197, 297, ... 14) 34, 43, 52, 61, ... ©u 82v0d1A3b rKGuNtram YSfo6fGt0wZazrCeL HLpLnCn.a 5 HAvlEll brFiWgGhptXsa NrLeksQeRr1vBendA.Q i RMSakdZeH 4wjiDtVhw gICnLfAiPnXibtJeG rAjlggdeDb4r1a7 u2E.v -1- Worksheet by Kuta Software LLC Find the common difference, the term named in the problem, and the explicit formula. 15) 17, 11, 5, −1, ... Find a39 16) 5, −5, −15, −25, ... Find a20 17) −40, −47, −54, −61, ... Find a29 18) −32, −132, −232, −332, ... Find a40 19) −8, 22, 52, 82, ... Find a20 20) 29, 38, 47, 56, ... Find a29 21) 36, 29, 22, 15, ... Find a29 22) −20, −29, −38, −47, ... Find a20 Determine if the sequence is geometric. If it is, find the common ratio. 23) −2, −10, −50, −250, ... 24) −1, 6, −36, 216, ... 25) −1, −5, −25, −125, ... 26) −2, 10, −50, 250, ... 1 1 27) −3, −1, − , − , ... 3 9 28) −2, ©D B210e1f36 0KSuBtlao SS4o5fXtGwoaIrpem GLkL5Co.D Y JA5lili ZrFi8gghotDsL UrlehsRe5rQv7egdM.U 7 EMqaMdMeN 4wci4t1hg KIunUfWi3nVistVeb sAjlTgZe8bJrCaz P2l.u -2- 1 1 1 , − , , ... 2 8 32 Worksheet by Kuta Software LLC Find the common ratio and the three terms in the sequence after the last one given. 29) −2, −8, −32, −128, ... 30) 2, −8, 32, −128, ... 31) 3, −6, 12, −24, ... 32) 2, 10, 50, 250, ... Find the common ratio and the recursive formula. 33) −1, 5, −25, 125, ... 34) −3, −15, −75, −375, ... 35) 3, −15, 75, −375, ... 36) 0.5, 1, 2, 4, ... Find the common ratio, the term named in the problem, and the explicit formula. 37) 4, 12, 36, 108, ... Find a9 38) −2, 6, −18, 54, ... Find a12 39) −3, 9, −27, 81, ... Find a10 40) −4, 8, −16, 32, ... Find a11 41) −4, −12, −36, −108, ... Find a12 42) 4, 8, 16, 32, ... Find a10 ©Q u2t0m1D33 BKbuptZa1 pS8o7fytfwtaAr6ew aLYLgCc.G f nABl4ly NrUiPgchIt9sQ Brleys8eMrPvYehdo.k T fMIaJdjem SwMiXtbhC vI3nAfeiTndiotReM 7A2ligBe4bordaG O2f.L -3- Worksheet by Kuta Software LLC 5 43) −20, −10, −5, − , ... 2 Find a9 44) 1 1 1 1 , , , , ... 2 6 18 54 Find a12 Given the first term and the common difference of an arithmetic sequence find the explicit formula and the three terms in the sequence after the last one given. 45) a1 = 35, d = −20 46) a1 = 22, d = −9 47) a1 = −34, d = −2 48) a1 = −22, d = −30 Given the first term and the common ratio of a geometric sequence find the explicit formula and the three terms in the sequence after the last one given. 49) a1 = 4, r = −4 50) a1 = −2, r = 4 51) a1 = 1, r = 3 52) a1 = −3, r = −5 Find the missing term or terms in each arithmetic sequence. 53) ..., −6, ___, 8, ... 54) ..., 30, ___, ___, 0, ... 55) ..., −14, ___, ___, 46, ... 56) ..., 38, ___, ___, 65, ... ©e D2q0q143I sKFultjaC PSUo9fxtHwMaarue8 aLnLYCS.L E 2Aelrl3 krYiAgHhTtYsU Zrkegsherrav8eXdW.z F sMsa3dpeY iwFiXtAhI WITn1f2i0nHiutMe6 iA4lFgBe3bdr0aQ V28.9 -4- Worksheet by Kuta Software LLC ID: 1 Secondary I Name___________________________________ 4.3 Arithmetic and Geometric Sequences Worksheet Period____ ©p V2v0X1L3r TKEuetAai ZS3oYftthw0aurjeb 3LYLlCD.O o 2AIl2lM YrUiVgAh0tcse rrzewsEeIrGvueBdt.9 Determine if the sequence is arithmetic. If it is, find the common difference. 1) −9, −109, −209, −309, ... 2) 28, 18, 8, −2, ... d = −100 d = −10 3) 28, 26, 24, 22, ... 4) −16, −6, 4, 14, ... d = −2 d = 10 5) −8, −4, 0, 4, ... 6) 1, d =4 1 1 , 0, − , ... 2 2 d =− 1 2 Find the common difference and the three terms in the sequence after the last one given. 7) −39, −33, −27, −21, ... 8) −27, −17, −7, 3, ... Common Difference: d = 6 Next 3 terms: −15, −9, −3 9) 17, 13, 9, 5, ... Common Difference: d = 10 Next 3 terms: 13, 23, 33 10) Common Difference: d = −4 Next 3 terms: 1, −3, −7 1 23 43 21 , , , , ... 5 15 15 5 4 3 83 103 41 Next 3 terms: , , 15 15 5 Common Difference: d = Find the common difference and the recursive formula. 11) 9, 19, 29, 39, ... 12) 22, 19, 16, 13, ... Common Difference: d = 10 Recursive: an = an − 1 + 10 Common Difference: d = −3 Recursive: an = an − 1 − 3 a1 = 9 a1 = 22 13) −3, 97, 197, 297, ... 14) 34, 43, 52, 61, ... Common Difference: d = 100 Recursive: an = an − 1 + 100 Common Difference: d = 9 Recursive: an = an − 1 + 9 a1 = −3 ©2 K2b0S1s38 SKvuNt5a8 bSToqfotswXavrqeF SLWL5Cv.4 d EAdlelK rrPiXgXh5tEsx tr5ersie8rKvyeFdG.8 G BMOa8d7ey 6wVi3tJhS oIOnNfgi0nfiytaeB 5ABlagreLbMrtaI K2t.7 a1 = 34 -1- Worksheet by Kuta Software LLC Find the common difference, the term named in the problem, and the explicit formula. 15) 17, 11, 5, −1, ... Find a39 16) 5, −5, −15, −25, ... Find a20 Common Difference: d = −6 a39 = −211 Common Difference: d = −10 a20 = −185 Explicit: an = 17 + (n − 1) ⋅ −6 Explicit: an = 5 + (n − 1) ⋅ −10 17) −40, −47, −54, −61, ... Find a29 18) −32, −132, −232, −332, ... Find a40 Common Difference: d = −7 a29 = −236 Common Difference: d = −100 a40 = −3932 Explicit: an = −40 + (n − 1) ⋅ −7 Explicit: an = −32 + (n − 1) ⋅ −100 19) −8, 22, 52, 82, ... Find a20 20) 29, 38, 47, 56, ... Find a29 Common Difference: d = 30 a20 = 562 Common Difference: d = 9 a29 = 281 Explicit: an = −8 + (n − 1) ⋅ 30 Explicit: an = 29 + (n − 1) ⋅ 9 21) 36, 29, 22, 15, ... Find a29 22) −20, −29, −38, −47, ... Find a20 Common Difference: d = −7 a29 = −160 Common Difference: d = −9 a20 = −191 Explicit: an = 36 + (n − 1) ⋅ −7 Explicit: an = −20 + (n − 1) ⋅ −9 Determine if the sequence is geometric. If it is, find the common ratio. 23) −2, −10, −50, −250, ... 24) −1, 6, −36, 216, ... r=5 25) −1, −5, −25, −125, ... r = −6 26) −2, 10, −50, 250, ... r=5 1 1 27) −3, −1, − , − , ... 3 9 r= r = −5 28) −2, 1 3 ©e J2S0n1E3Z 6KZuqtHa4 4SvoBf9thwOavrUez ELlLoCi.S u LA0l8lP 4rGiggvhYt5sF mrOeasJeErev6eMdB.o s JMyaQdUeN EwaiFtshx PIBnBfkixnmiztfeF vAElVgXeYborMa6 42V.5 1 1 1 , − , , ... 2 8 32 r=− -2- 1 4 Worksheet by Kuta Software LLC Find the common ratio and the three terms in the sequence after the last one given. 30) 2, −8, 32, −128, ... 29) −2, −8, −32, −128, ... Common Ratio: r = 4 Next 3 terms: −512, −2048, −8192 31) 3, −6, 12, −24, ... Common Ratio: r = −4 Next 3 terms: 512, −2048, 8192 32) 2, 10, 50, 250, ... Common Ratio: r = −2 Next 3 terms: 48, −96, 192 Common Ratio: r = 5 Next 3 terms: 1250, 6250, 31250 Find the common ratio and the recursive formula. 33) −1, 5, −25, 125, ... 34) −3, −15, −75, −375, ... Common Ratio: r = −5 Recursive: an = an − 1 ⋅ −5 Common Ratio: r = 5 Recursive: an = an − 1 ⋅ 5 a1 = −1 a1 = −3 35) 3, −15, 75, −375, ... 36) 0.5, 1, 2, 4, ... Common Ratio: r = −5 Recursive: an = an − 1 ⋅ −5 Common Ratio: r = 2 Recursive: an = an − 1 ⋅ 2 a1 = 3 a1 = 0.5 Find the common ratio, the term named in the problem, and the explicit formula. 37) 4, 12, 36, 108, ... Find a9 38) −2, 6, −18, 54, ... Find a12 Common Ratio: r = 3 a9 = 26244 Common Ratio: r = −3 a12 = 354294 n−1 Explicit: an = −2 ⋅ (−3) Explicit: an = 4 ⋅ 3 39) −3, 9, −27, 81, ... Find a10 40) −4, 8, −16, 32, ... Find a11 Common Ratio: r = −3 a10 = 59049 Explicit: an = −3 ⋅ (−3) Common Ratio: r = −2 a11 = −4096 n−1 41) −4, −12, −36, −108, ... Find a12 Explicit: an = −4 ⋅ (−2) Common Ratio: r = 2 a10 = 2048 n−1 ©1 x2J0t193r 4K6u7thaF LSKosfYtBwFaWrxes yLULtCO.o Y oAjlKl5 HrTi5gZh0tlsl hrJeXsAe8r3v8eddj.9 l LM7abdKey JwmintYhF jI1nlfZidnJi8tLeo MA9ldgteNburfah g26.6 n−1 42) 4, 8, 16, 32, ... Find a10 Common Ratio: r = 3 a12 = −708588 Explicit: an = −4 ⋅ 3 n−1 Explicit: an = 4 ⋅ 2 -3- n−1 Worksheet by Kuta Software LLC 5 1 43) −20, −10, −5, − , ... Common Ratio: r = 2 2 5 Find a9 a9 = − 64 1 Explicit: an = −20 ⋅ 2 () 44) n−1 1 1 1 1 1 , , , , ... Common Ratio: r = 2 6 18 54 3 1 Find a12 a12 = 354294 1 1 n−1 Explicit: an = ⋅ 2 3 () Given the first term and the common difference of an arithmetic sequence find the explicit formula and the three terms in the sequence after the last one given. 45) a1 = 35, d = −20 46) a1 = 22, d = −9 Next 3 terms: 15, −5, −25 Explicit: an = 35 + (n − 1) ⋅ −20 47) a1 = −34, d = −2 Next 3 terms: 13, 4, −5 Explicit: an = 22 + (n − 1) ⋅ −9 48) a1 = −22, d = −30 Next 3 terms: −36, −38, −40 Explicit: an = −34 + (n − 1) ⋅ −2 Next 3 terms: −52, −82, −112 Explicit: an = −22 + (n − 1) ⋅ −30 Given the first term and the common ratio of a geometric sequence find the explicit formula and the three terms in the sequence after the last one given. 49) a1 = 4, r = −4 50) a1 = −2, r = 4 Next 3 terms: −16, 64, −256 n−1 Explicit: an = 4 ⋅ (−4) 51) a1 = 1, r = 3 Next 3 terms: −8, −32, −128 n−1 Explicit: an = −2 ⋅ 4 52) a1 = −3, r = −5 Next 3 terms: 3, 9, 27 n−1 Explicit: an = 3 Next 3 terms: 15, −75, 375 n−1 Explicit: an = −3 ⋅ (−5) Find the missing term or terms in each arithmetic sequence. 53) ..., −6, ___, 8, ... 54) ..., 30, ___, ___, 0, ... 1 55) ..., −14, ___, ___, 46, ... 20, 10 56) ..., 38, ___, ___, 65, ... 6, 26 ©Z J2F03183J NKEurtTa6 ZSVohf0tiwxaArhee mLuL8CO.m Z GA1lIle 3rsiKg8hctRsK brce1sfesrcvTe6d1.Z e 6MkaCdIe2 dw5ietnhl 7IQngfli2nGixtlec AAUlngVeXbErWa9 I2U.N 47, 56 -4- Worksheet by Kuta Software LLC