H(1)= 9

h(n)=h(n−1)⋅(-3)

Find an explicit formula for h(n).

h(n)= ?

​

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 .

y - y1 = m(x- x1)

y - (-5) = 2/3(x -0)

y + 5 = 2/3x

y = 2/3x - 5

its the fourth option