Question

Complete the recursive formula of the arithmetic sequence -3, -1, 1, 3,...

Answer 1

Given:

The given arithmetic sequence is:

$-3,-1,1,3,...$

To find:

The recursive formula of the given arithmetic sequence.

Solution:

We have,

$-3,-1,1,3,...$

Here, the first term is -3. So, $b(1)=-3$.

The common difference is:

$d=-1-(-3)$

$d=-1+3$

$d=2$

The recursive formula of an arithmetic sequence is:

$b(n)=b(n-1)+d$

Where, d is the common difference.

Putting $d=2$, we get

$b(n)=b(n-1)+2$

Therefore, the recursive formula of the given arithmetic sequence is $b(n)=b(n-1)+2$, where $b(1)=-3$.