Question

Write an recursive formula for An, the nth term of the sequence 5, -2, -9,

Answer 1

Given:

The given sequence is:

$5,-2,-9,...$

To find:

The recursive formula for $a_n$, the nth term of the sequence.

Solution:

We have,

$5,-2,-9,...$

Here, the first term is 5.

$-2-5=-7$

$-9-(-2)=-9+2$

$-9-(-2)=-7$

The common difference is -7.

The recursive formula for the nth term of the sequence is

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

Where, $d$ is the common difference.

Putting $d=-7$ in the above formula, we get

$a_n=a_{n-1}+(-7)$

$a_n=a_{n-1}-7$

Therefore, the recursive formula for the nth term of the sequence is $a_n=a_{n-1}-7$.