Question

(h(1) = 96 (h(n) = h(n − 1) - 1 Find an explicit formula for h(n).

Answer 1

Answer:

$a_n=97-n$

Step-by-step explanation:

Given:

$h(1)=96\\ \\h(n)=h(n-1)-1$

Find first terms:

$h(1)=96\\ \\h(2)=h(2-1)-1=h(1)-1=96-1=95\\ \\h(3)=h(3-1)-1=h(2)-1=95-1=94\\ \\h(4)=h(4-1)-1=h(3)-1=94-1=93\\ \\....$

In this arithmatic sequence, each next term is 1 less than the previous term.

The general explicit formula is

$a_n=a_1+(n-1)d$

In your case,

$a_1=96\ \text{ First term}\\ \\d=-1\ \text{ Common difference}$

Then

$a_n=96+(n-1)\cdot (-1)\\ \\a_n=96-(n-1)\\ \\a_n=96-n+1\\ \\a_n=97-n$