Question

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

b(1)= "answer"
b(n)=b(n-1)+ "answer"

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`.