Answer:
a. a[1] = 3; a[n] = 2a[n-1]
b. a[n] = 3·2^(n-1)
c. a[15] = 49,152
Explanation:
Each term of the given sequence is 2 times the previous term. (This description is the basis of the recursive formula.) That is, the terms of the given sequence have a common ratio of 2. This means the sequence is geometric, so the formulas for explicit and recursive rules for a geometric sequence apply.
The first term is 3, and the common ratio is 2.
(a)
The recursive rule is ...
a[1] = 3
a[n] = 2×a[n-1]
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(b)
The explicit rule is ...
a[n] = a[1]×r^(n-1)
a[n] = 3×2^(n-1)
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(c)
The 15th term is ...
a[15] = 3×2^(15-1) = 3×2^14
a[15] = 49,152