Sequences and Series Problem Solving
Explore a variety of sequence and series problems including loan repayment calculations, geometric series sums, convergence checks, and explicit sequence formula derivation. Test your mathematical knowledge and problem-solving skills with these challenging questions.
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A student borrowed $4000 for college expenses. The loan was repaid over a 100 month period, with monthly payments as follows: $60.00, $59.80, $59.60, ., $40.20 How much did the student pay over the life of the loan? 5010 $ A. C. 1010 $ D. 10 $ 020 , 4040 $ B.
The first three terms of the sequence are 4, -48, 576 Give an explicit formula for this sequence. A. C. = = 1 1 n n 4 ( 12 ) 12 ( 4 ) g g n n = D. 4 g = + 4 ( 1 )( 12 ) gn n B. 1 , 2 n = 12 g g n 1 n
The sum of the first eight terms of a geometric series is 4920. The common ratio is -3. Find g1. 2 5 . 1 A. C. 5 . 2 5 . 1 D. B.
Is the series 7 + 5.6 + 4.48 + convergent? If so, give its sum. ; 35 convergent A. C. not convergent D. ; 0 8 . ; convergent convergent B.
Calculate the sum of the integers from 308 to 511. 20 910 , 20 706 , A. C. 83 129 , 83 538 , D. B.
Give the limit of the sequence , , , 1 2 n + , ..., 7 19 3 12 16 36 64 2 4 n 1 DNE A. C. 4 1 3 D. B.
Suppose that a model airplane collection valued now at $2,500 increases .5% in value each month. Give the value of the collection in three years , 2 $ 537 69 . , 2 $ 976 82 . A. C. D. , 2 $ 991 70 . 13 $ 790 , 04 . B.
Give the limit of the sequence 80 , 60 , 45 , 33 75 . the geometric sequence 0 DNE A. C. 75 . 1 D. B.
Determine whether the sequence converges. If so, find its sum. 15 + 9 +27 5+81 25+ . A. Does not converges C. , 37 5 . Converges D. , B. , 45 5 . 22 5 . Converges Converges
Give a explicit formula for the sequence defined by = , 1 600 b 1 = (. 75 ) for n 1 b b 1 n n = = 1 1 n n (. 75 , 1 )( 600 ) , 1 600 (. 75 ) A. C. n b n b = n (. 75 , 1 )( 600 ) n b D. = n , 1 600 (. 75 ) n b B.
What is the position of 1954 in the arithmetic sequence 8, 15, 22, ., 1954, .? 279 198 A. C. 302 320 D. B.
n 8 Does the series converge? = n 1 9 If so, what is its value. 8 ; converges A. C. does not converge 9 ; 8 converges D. ; 9 converges B.
1 n 2 Does the series converge? = 1 n 6 3 If so, what is its value. ; 18 converges A. C. does not converge 2 ; 18 converges D. ; converges B. 3
Suppose that an employee earns $23,000 in the first year on the job. Each year thereafter, the employee received a raise of $2,500. Find the total amount the employee earns in 8 years. 216 $ 000 , 254 $ 000 , A. C. D. 297 $ 000 , 46 $ 250 , B.
A theater has 15 seats in the first row and 3 more seats in each subsequent row. If the last row has 27 seats, how many total seats are in the theater? 98 104 A. C. 101 105 D. B.
One sunflower produces 500 seeds. Each seed produces a flower which produces 500 seeds, and so on. Let an = the number of seeds after n generations. Write an explicit formula for an. = 500 a 1 = 1 n a 500 500 ( ) A. C. = 500 1 a a for n n 1 n n = 500 a 1 D. = 500 + 500 an n B. = + 500 1 a a for n 1 n n
Evaluate the series given. (5u-v) + (4u + v) + (3u + 3v) + + (23v 7u) 143 144 v 13 v 13 u u A. C. 143 D. 144 v 18 v 18 u u B.
Give the limit of the sequence , , , 1 2 + , ..., 16 23 7 n 11 16 24 32 8 n 1 DNE A. C. 8 7 1 D. B.
Calculate the monthly payment necessary to pay off a $25,000 car loan when given an annual rate of 4.5% and 60 monthly payments. 510 $ 17 . A. C. 417 $ 14 . D. 466 $ 08 . 1578 $ 13 . B.
Evaluate = 1 k 100 2 ( 13 ) k 8787 A. 187 C. D. , 8 800 11 , 400 B.
Give a recursive formula for the sequence defined by An 64 = 14 n = = 64 a 64 a a a 1 1 A. C. 1 = = 14 for n 14 for n 1 a a 1 n n n n = a = a 14 14 a a 1 1 D. 1 B. = + = + 64 for n 1 64 for n a a 1 n n n n
A family has lived in the same apartment for eight years. Their monthly rent the first year was $625. Each year thereafter their landlord raised their rent by $20 per month. In total, how much rent did they pay over the eight year period? 32 $ 160 , A. C. 765 $ D. , 2 $ 680 66 $ 720 , B.
One sunflower produces 500 seeds. Each seed produces a flower which produces 500 seeds, and so on. Let an = the number of seeds after n generations. Write a recursive formula for an. = 500 a 1 = 1 n a 500 500 ( ) A. C. = 500 1 a a for n n 1 n n = 500 a 1 D. = 500 + 500 an n B. = + 500 1 a a for n 1 n n
