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Unformatted text preview: Miller, Kierste Homework 10 Due: Apr 4 2007, 3:00 am Inst: Gary Berg 1 This printout should have 16 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Find a formula for the general term a n of the sequence n 1 , 6 , 11 , 16 , ... o assuming that the pattern of the first few terms continues. 1. a n = 4 n 3 2. a n = n + 5 3. a n = 5 n 4 correct 4. a n = n + 4 5. a n = 6 n 5 Explanation: In the sequence n 1 , 6 , 11 , 16 , ... o each term is larger than the preceding one by 5, so a n = a 1 + d ( n 1) = 1 + 5( n 1) . Consequently, a n = 5 n 4 . keywords: 002 (part 1 of 1) 10 points Find a formula for the general term a n of the sequence n 1 , 5 4 , 25 16 , 125 64 , ... o assuming that the pattern of the first few terms continues. 1. a n =  5 4 n 1 correct 2. a n =  4 5 n 1 3. a n = 5 4 n 4. a n = 6 5 n 5. a n = 4 5 n 6. a n =  6 5 n 1 Explanation: In the sequence n 1 , 5 4 , 25 16 , 125 64 , ... o each term is 5 4 times the preceeding one, i.e. , a n =  5 4 a n 1 . Consequently, a n =  5 4 n 1 since a 1 = 1. keywords: sequence, exponential 003 (part 1 of 1) 10 points Determine if the sequence { a n } converges, and if it does, find its limit when a n = 4 n 5 2 n 3 + 5 3 n 4 + 4 n 2 + 5 . 1. limit = 1 2. limit = 4 3 Miller, Kierste Homework 10 Due: Apr 4 2007, 3:00 am Inst: Gary Berg 2 3. limit = 0 4. the sequence diverges correct 5. limit = 1 2 Explanation: After division by n 4 we see that a n = 4 n 2 n + 5 n 4 3 + 4 n 2 + 5 n 4 . Now 2 n , 5 n 4 , 4 n 2 , 5 n 4 as n ; in particular, the denominator converges and has limit 3 6 = 0. Thus by properties of limits { a n } diverges since the sequence { 4 n } diverges. keywords: 004 (part 1 of 1) 10 points Determine whether the sequence { a n } con verges or diverges when a n = 8 n 2 4 n + 1 2 n 2 + 7 n + 1 , and if it does, find its limit 1. limit = 1 2 2. limit = 0 3. the sequence diverges 4. limit = 3 4 5. limit = 3 2 correct Explanation: After bringing the two terms to a common denominator we see that a n = 8 n 3 + 8 n 2 (4 n + 1)...
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 Spring '08
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