Lesson 3 Homework - Geometric Sequences E d200j1j2v nkuuotsa6 7Suo4fItbwuaSr6ei YLJLoCj.c 4 oaqlxla wrqiyg8hctdsn lriens8edrpvpeod h.

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1 11) 23, -46, 92,... ; find t 10 12) 2, 1 2, 1 8,... ; find t 5-1- f h220a1b2j KKKurtQan isoozfmtgw2aprpex ILjLxCr.2 W IA7lilm ErFi1gChbtdsl ir2efsmemrnvkezdq.i 0 xm9asdqei uwsiltbhq IIHnNfkiPn5iztXeL wawligse9byrsaj k1o.w Worksheet by Kuta Software LLC MATH 11 - Pre Calculus UNIT: Series & Sequences ID: 1 Name Lesson 3 Homework - Geometric Sequences E d200j1j2v nkuuotsa6 7Suo4fItbwuaSr6ei YLJLoCj.c 4 oaqlxla wrqiyg8hctdsn lriens8edrpvpeod h.3 Circle the sequences that are geometric. If the sequence is geometric state its common ratio. 1) 1, 2, 4, 8, 16,... 2) 4, 9, 16, 25, 36,... Date Period 3) -3, 2, 7, 12, 17,... 4) 6, 0.6, 0.06, 0.006,... State the common ratio, then write the next 3 terms of the sequence. 5) -1, -3, -9,... 6) 4, -2, 1,... 7) 48, 24, 12,... 8) 1 2, 1 6, 1 18,... For each geometric sequence, determine the indicated value. 9) 3, 6, 12,... ; find t 7 10) 18, 9, 4.5,... ; find t 6 Using the given information, identify each geometric series as either increasing or decreasing. 13) r = 4, t 1 = 3 14) r = 2, t 1 = 5 15) r = 0.5, t 1 = 3 16) r = 1 3, t 1 = 9 Create the first 5 terms of a geometric sequence where: 17) the 6th term is 64 18) the 1st term is 3 4

2 -2- u o2k0f1v2x SKNuptbaM MSNoyfztZwya7rhen DL7LICg.e L fa1lxlm jr Yisgch5tss1 rr3edsieerjvoezd0.i a jmjatdfej Cwxiztoh9 2IOn6fziAnhiQtGeV FAwl8gJejbYr 2aF 01o.z Worksheet by Kuta Software LLC 19) every term is negative 20) every term is an even number Use the given data about each finite geometric series to determine the indicated values. 21) t 1 = 1, r = 2 22) t 1 = and t 4 = 2 a) Find t 9 a) Find t 7 b) The last term is How many terms are in the sequence? b) Which term has the value ? The first term in a sequence is 8 and the last term is 128 and there are 5 terms in the sequence. 23) If it is an arithmetic sequence, find the three 24) If it is a geometric sequence, find the three In a geometric sequence, t 3 = 9 and t 6 = ) Find t 7 26) Find t 9

3 -3- Y 92Z0R1o2y HKDuNtmaS RSro1fvtFw2amrteu 4L7LfCJ.T R VA8lulk kroifgchutgsu wrxersoetrkvietdk.u Y umjamd1e2 twqi0tohf tiqnkf5iwnaibtee3 LAjlMgjezberoac B1E.y Worksheet by Kuta Software LLC Solve the following problems. 27) If an arithmetic sequence and a geometric sequence have the same first term, and the common difference is equal to the common ratio (which is greater than 1), which will increase more rapidly as more terms are added? 28) A farmer wants to estimate the value of a new tractor a few years after its purchase. A new tractor worth $ depreciates in value by about 10% each year. Estimate the value of the tractor at the end of each of the first 5 years.

4 MATH 11 - Pre Calculus UNIT: Series & Sequences ID: 1 Name Lesson 3 Homework - Geometric Sequences o B2O0b182 t ZK7u6tAaR jsiotfetaw6anriey SLCLbCZ.8 z eablulb Pr1i4gGhct ns8 1r5ewsUejrBvJePdi.v Circle the sequences that are geometric. If the sequence is geometric state its common ratio. Date Period 1) 1, 2, 4, 8, 16,... r = 2 3) -3, 2, 7, 12, 17,... Not geometric 2) 4, 9, 16, 25, 36,... Not geometric 4) 6, 0.6, 0.06, 0.006,... r = 0.1 State the common ratio, then write the next 3 terms of the sequence. 5) -1, -3, -9,... r = 3 ;..., -27, -81, -243,... 7) 48, 24, 12,... r = 0.5 ;..., 6, 3, 1.5,... 6) 4, -2, 1,... r = -0.5 ;..., -0.5, 0.25, ,... 8) 1 2, 1 6, 1 18,... r = 1 3 ; , 1 162, 1 486,... For each geometric sequence, determine the indicated value. 9) 3, 6, 12,... ; find t ) 18, 9, 4.5,... ; find t ) 23, -46, 92,... ; find t ) 2, 1 2, 1 8,... ; find t Using the given information, identify each geometric series as either increasing or decreasing. 13) r = 4, t 1 = 3 decreasing 15) r = 0.5, t 1 = 3 decreasing 14) r = 2, t 1 = 5 increasing 16) r = 1 3, t = 9 1 increasing Create the first 5 terms of a geometric sequence where: 17) the 6th term is 64 answers will vary EX: 2, 4, 8, 16, 32, 64,... 18) the 1st term is 3 4 answers will vary EX: 3 4, 3 8, 3 16, 3 32, 3 64, z Y2h0Q1J2n XKjuJtHa6 3S4oGfhtuwdazrled WLVLCCM.T x 8AJlVlb zrjiig4hetnsq vrhe4sde6rmvzeldx.a F XMlaGdmeG 2wziXtahw niinnfbimnsiztneh HAulygze4borraS n1b.3 Worksheet by Kuta Software LLC

5 -2-4 w2r011w2z nkluvtta9 YSQo8f3tbwIaMrceW ELtLyCR.R i eakl7ln Zr Ui6gMhxtHsp mrnefs4emrmvdewdd.f Z fmiajdden twsihtrhq hionmfrisnsiqtnew favllgaejbrrza4 T11.Z Worksheet by Kuta Software LLC 19) every term is negative 20) every term is an even number answers will vary EX: -1, -3, -9, -27, -81,... answers will vary EX: 2, 8, 16, 32, 64,... Use the given data about each finite geometric series to determine the indicated values. 21) t 1 = 1, r = 2 22) t 1 = and t 4 = 2 a) Find t 9 a) Find t 7 b) The last term is How many terms are in the sequence? b) Which term has the value ? t 7 = 2000 and t 8 = t 9 = 256, There are 13 terms in the sequence. The first term in a sequence is 8 and the last term is 128 and there are 5 terms in the sequence. 23) If it is an arithmetic sequence, find the three 38, 68, 98 24) If it is a geometric sequence, find the three 16, 32, 64 In a geometric sequence, t 3 = 9 and t 6 = ) Find t ) Find t

6 -3- G G2X0F1z2J BKTuNtDar PSko6f7t5wWaprxec DL3LNCY.s h 6Abl5lM 8reiQghh0tCsX 0rReUsRefrHvGe6d9.u i fmvahdhey Nwli9t4h8 kihn5fqionnistpeh AALl4gUecbJrEan 51H.I Worksheet by Kuta Software LLC Solve the following problems. 27) If an arithmetic sequence and a geometric sequence have the same first term, and the common difference is equal to the common ratio (which is greater than 1), which will increase more rapidly as more terms are added? geometric sequence 28) A farmer wants to estimate the value of a new tractor a few years after its purchase. A new tractor worth $ depreciates in value by about 10% each year. Estimate the value of the tractor at the end of each of the first 5 years. Y1 = $ Y2 = $ Y3 = $ Y4 = $242