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

Question

asked Dec 23, 2022 141k views

1 Answer

Marlina · Answer 1 · 2022-12-27T21:53:33+0000

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
.