University:
University of Central Arkansas
Course:
MATH 3364 | Concepts of Geometry and Measurement
Academic year:

2024
Views:

83

Pages:

2
Author:

Gilbert Pineda

Pre-Calculus 11 Geometric Sequences & Series Practice 1. Is each sequence geometric? If it is, state the common ratio and a formula to determine the general term in the form tn = t1rn – 1. a) 11, 33, 99, 297, … b) 6, 12, 18, 24, … c) How much will the digger be worth in 7 years? d) How long will it take before the equipment is worth less than $120 000? 2. Write the first four terms of each geometric sequence. 1 a) t1 = –8, r = 2 n–1 b) tn = 3(0.6) 9. For each geometric series, state the values of t1 and r. Then, determine each partial sum. a) 0.43 + 0.0043 + 0.000 043 + …, (S6) b) 5 – 5 + 5 – …, (S10) 3. Determine the number of terms in each geometric sequence. a) 4, 12, 36,  , 78 732 1 5 b) t1 = 5, r =  , tn = 2 64 10. Determine the partial sum, Sn, for each geometric series described. a) t1 = –4, r = 2, n = 10 b) tn = (–5)(0.5)n – 1 , n = 5 11. Determine the partial sum, Sn, for each geometric series. 4. Determine the nth term of each geometric a) 2 + 6 + 18 +  + 354 294 sequence. b) t1 = –3, r = –2, tn = 6144 a) 6, –18, 54, –164, … 12. Determine the first term for each geometric b) t1 = 7, t5 = 1792 series. 5. Determine the unknown terms in each geometric sequence. a) Sn = 3932.4, tn = 4915.2, r = –4 b) Sn = 292 968, n = 8, r = 5 a) 18, , , 6174 b) , 4, , , 108 6. Determine the first term, the common ratio, and an expression for the general term of each geometric sequence. a) t5 = 900, t7 = 0.09 b) t3 = –1728, t6 = 373 248 7. The following sequences are geometric. What is the value of each variable? a) 8x – 12, 16, 64, 256, … b) 25, 5, 1, 2y – 1, … 8. An excavating company has a digger that was purchased for $240 000. It is depreciating at 12% per year. a) Determine the next three terms of this geometric sequence. b) Determine the general term. Define your variables. 13. Determine the number of terms in each geometric series. a) 4 + 20 + 100 +  + tn = 15 624 b) 1792 – 896 + 448 –  – tn = 1197 14. The fourth term of a geometric series is 30; the ninth term is 960. Determine the sum of the first nine terms. 15. The first term of a geometric series is 3. The sum of the first two terms of the series is 15 and the sum 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 vertical height that is 3 the previous height. Determine 5 the total vertical distance travelled by the ball when it contacts the ground for the sixth time. Express your answer to the nearest tenth of a metre. Pre-Calculus 11 Geometric Sequences & Series Practice Key 1. a) geometric, r = 3, tn = 11(3)n – 1 b) not geometric 2. a) –8, –4, –2, –1 b) 3, 1.8, 1.08, 0.648 3. a) 10 b) 7 4. a) tn = 6(–3) n – 1 b) tn = 7(4)n – 1 4 5. a) 126, 882 b) , 12, 36 3 6. a) t1 = 9  1010, r = 0.01, tn = (9  1010 )(0.01)n – 1 b) t1 = –48, r = –6, tn = (–48)(–6)n – 1 7. a) x = 2 b) y = 6 or 3 10 5 8. a) $211 200, $185 856, $163 553 b) tn = 240 000(0.88) n – 1, tn = value of digger, in dollars, n – 1 = years since purchase c) $98 082 d) 6 years 9. a) t1 = 0.43, r = 0.01, S6 = 43 99 b) t1 = 5, r = –1, S10 = 0 10. a) –4092 b) 155 16 11. a) 531 440 b) 4095 12. a) 1.2 b) 3 13. a) 6 b) 9 14. 1916.25 15. 4 16. 94.2 m

Geometric Sequences and Series Practice with key

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