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

H(1)= 9h(n)=h(n−1)⋅(-3)Find an explicit formula

lucy143

18.04.2021

Given:

h(1)=9

$h(n)=h(n-1)\cdot (-3)$

To find:

The explicit formula for h(n).

Solution:

We have,

$h(n)=h(n-1)\cdot (-3)$ ...(i)

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

$a(n)=a(n-1)\cdot r$ ...(ii)

where r is the common ratio.

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

r=-3

We have, h(1)=9 so the first term of the geometric sequence is a=9 .

The explicit formula for a geometric sequence is:

$h(n)=ar^{n-1}$

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

$h(n)=9(-3)^{n-1}$

Therefore, the required explicit formula is $h(n)=9(-3)^{n-1}$ .

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