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These are the first six terms of a sequence starting with a1=8: 8, 6, 9 2 , 27 8 , 81 32 , 243 128 , ... Find a recursive formula for this sequence that is valid for n>1.

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Final answer:

The recursive formula for the given sequence is an = an-1 * (2n - 1)/(n - 1).

Step-by-step explanation:

The given sequence is: 8, 6, 9 2, 27 8, 81 32, 243 128, ...

In order to find a recursive formula for this sequence, we need to look for a pattern. Taking a closer look, we can see that each term is obtained by multiplying the previous term by a fraction: for example, the second term (6) is obtained by multiplying the first term (8) by 6/8, the third term (9 2) is obtained by multiplying the second term (6) by 9/2, and so on.

Therefore, the recursive formula for this sequence is: an = an-1 * (2n - 1)/(n - 1).

User Michael Soliman
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