Question

Write a recursive formula and an explicit formula for the following arithmetic sequence: -1,6,13,20,27

Answer 1

Recursive formula is:
`a_1=-1 ; \ \ a_n=a_(n-1)+7`

Explicit formula is:
`a_n=7n-8`

Explanation:

We need to find recursive formula and explicit formula for arithmetic sequence -1,6,13,20,27

In the given sequence First term a₁= -1

Common difference d = 7

Finding Recursive Formula

The recursive formula is of type:
`a_1= First \ term` and
`a_n=a_(n-1)+d`

Since the First term a₁ is -1 and common difference d is 7 so, the recursive formula for given arithmetic sequence will be:

`a_1=-1 ; \ \ a_n=a_(n-1)+7`

Finding Explicit Formula

The explicit formula is of type:
`a_n=a_1+(n-1)d`

We have

First term a₁= -1

Common difference d = 7

So, explicit formula will be:

`a_n=-1+(n-1)7\\a_n=-1+7n-7\\a_n=7n-8`

So, explicit formula is:
`a_n=7n-8`