Pre-Calculus 11 Geometric Sequences & Series Practice 1. Is each ...

Pre-Calculus 11Geometric Sequences & Series Practice1. Is each sequence geometric? If it is, state thecommon ratio and a formula to determine thegeneral term in the form t n = t 1 r n – 1 .a) 11, 33, 99, 297, …b) 6, 12, 18, 24, …2. Write the first four terms of each geometricsequence.a) t 1 = –8, r = 1 2b) t n = 3(0.6) n – 13. Determine the number of terms in eachgeometric sequence.a) 4, 12, 36, , 78 732b) t 1 = 5, r =1 , t n = 5 2 644. Determine the nth term of each geometricsequence.a) 6, –18, 54, –164, …b) t 1 = 7, t 5 = 17925. Determine the unknown terms in each geometricsequence.a) 18, , , 6174b) , 4, , , 1086. Determine the first term, the common ratio, andan expression for the general term of eachgeometric sequence.a) t 5 = 900, t 7 = 0.09b) t 3 = –1728, t 6 = 373 2487. The following sequences are geometric. What isthe value of each variable?a) 8x – 12, 16, 64, 256, …b) 25, 5, 1, 2y – 1, …8. An excavating company has a digger that waspurchased for $240 000. It is depreciating at12% per year.a) Determine the next three terms of thisgeometric sequence.b) Determine the general term. Define yourvariables.c) How much will the digger be worth in7 years?d) How long will it take before the equipmentis worth less than$120 000?9. For each geometric series, state thevalues of t 1 and r. Then, determine each partialsum.a) 0.43 + 0.0043 + 0.000 043 + …, (S 6 )b) 5 – 5 + 5 – …, (S 10 )10. Determine the partial sum, S n , for eachgeometric series described.a) t 1 = –4, r = 2, n = 10b) t n = (–5)(0.5) n – 1 , n = 511. Determine the partial sum, S n , for eachgeometric series.a) 2 + 6 + 18 + + 354 294b) t 1 = –3, r = –2, t n = 614412. Determine the first term for each geometricseries.a) S n = 3932.4, t n = 4915.2, r = –4b) S n = 292 968, n = 8, r = 513. Determine the number of terms in eachgeometric series.a) 4 + 20 + 100 + + t n = 15 624b) 1792 – 896 + 448 – – t n = 119714. The fourth term of a geometric series is 30; theninth term is 960. Determine the sum of thefirst nine terms.15. The first term of a geometric series is 3. The sumof the first two terms of the series is 15 and thesum of the first three terms of the series is 63.Determine the common ratio.16. A ball is dropped from the top of a 25-m ladder.In each bounce, the ball reaches a verticalheight that is 3 the previous height. Determine5the total vertical distance travelled by the ballwhen it contacts the ground for the sixth time.Express your answer to the nearest tenthof a metre.

Pre-Calculus 11Geometric Sequences & Series PracticeKey1. a) geometric, r = 3, t n = 11(3) n – 1 b) not geometric2. a) –8, –4, –2, –1 b) 3, 1.8, 1.08, 0.6483. a) 10 b) 74. a) t n = 6(–3) n – 1 b) t n = 7(4) n – 15. a) 126, 882 b) 4 , 12, 3636. a) t 1 = 9 10 10 , r = 0.01,t n = (9 10 10 )(0.01) n – 1b) t 1 = –48, r = –6, t n = (–48)(–6) n – 17. a) x = 2 b) y = 610 or 3 58. a) $211 200, $185 856, $163 553b) t n = 240 000(0.88) n – 1 , t n = value of digger,in dollars, n – 1 = years since purchasec) $98 082 d) 6 years9. a) t 1 = 0.43, r = 0.01, S 6 = 4399b) t 1 = 5, r = –1, S 10 = 010. a) –4092 b)1551611. a) 531 440 b) 409512. a) 1.2 b) 313. a) 6 b) 914. 1916.25 15. 416. 94.2 m