Question

Find an explicit formula for the sequence given by the recursive definition. t_n = t_n-1 + 4, t_1= 6

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Answer 1

`\text{d. }t_n=2+4n`

Explanation:

The added 4 in the recursive formula tells you that the common difference between terms is 4. That means the explicit formula will have a 4n term in it (matching choices A and D). Of those, only choice D has a first-term value of 6 for n=1.

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You know the explicit formula for and arithmetic sequence is ...

tn = t1 +d(n -1)

The recursive formula tells you the first term is t1=6, and the common difference is d=4. Then the explicit formula is ...

tn = 6 +4(n -1)

tn = 2 +4n . . . . . matches choice D