## h(1)= 9 h(n)=h(n−1)⋅(-3) Find an explicit formula for h(n). h(n)= ?

Question

h(1)= 9

h(n)=h(n−1)⋅(-3)

Find an explicit formula for h(n).

h(n)= ?

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Mathematics
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2021-07-22T17:01:01+00:00
2021-07-22T17:01:01+00:00 1 Answers
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## Answers ( )

Given:To find:The explicit formula for h(n).

Solution:We have,

…(i)

It is the recursive formula of a geometric sequence. It is of the form

…(ii)

where r is the common ratio.

On comparing (i) and (ii), we get

We have, so the first term of the geometric sequence is .

The explicit formula for a geometric sequence is:

Substitute a=9 and r=-3 to get the explicit formula for the given sequence.

Therefore, the required explicit formula is .