Question

Find the explicit formula for a 1 =-4,a n =a n-1 +9,n>=2

Answer 1

Given:

$a_1=-4$ and $a_n=a_{n-1}+9$ where $n\geq 2$.

To find:

The explicit formula for the given recursive formula.

Solution:

We know that recursive formula of an AP is:

$a_n=a_{n-1}+d$

Where, d is the common difference.

We have,

$a_n=a_{n-1}+9$

Here, d=9.

The first term of the AP is $a_1=-4$.

The explicit formula for an AP is:

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

Substituting $a_1=-4$ and $d=9$, we get

$a_n=-4+(n-1)9$

$a_n=-4+9n-9$

$a_n=-13+9n$

Therefore, the required explicit formula for the given sequence is $a_n=-13+9n$.