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1. Give recursive definitions of each of the following sequences:
(a) 1, 5, 52 , 53 , 54 , ..
(b) 1, 1, 1, 1, ...
(c) 1, −1, 2, −2, 3, −3, 4, −4, 5, −5, 6, ...
(d) 2, 1, 3, 4, 7, 11, 18, 29, 47
(e) 1, 2, 7, 20, 61, 182, 547, 1640, 4921, 14762, 44287, ... 2. 3. Let a1 , a2 , a3 , ... be a sequence given by a1 = 1 and an = 2an−1 + 1
Determine the first 6 terms of the sequence and the formula for an . 2
4. Let a1 , a2 , a3 , ... be a sequence given by a1 = 1 and an+1 = (n + 1) – an Determine the first 6 terms of the sequence and the formula for an . 5. Let a1 , a2 , a3 , ... be a sequence given by a1 = 0, a2 = 1 and an = 4an−2
Determine the first 6 terms of the sequence and the formula for an . 6. Rank the following by growth rate (prove any relations as needed):
n, n1/2 , log n, log(log(n)), log2 n, (1/3)n , π, n!, en , n2 7. 8.

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