Question

What is the recursive formula for this arithmetic sequence? –7, –1, 5, 11, ...

Answer 1

`a_(n)= a_(n-1) + 6`

Explanation:

–7, –1, 5, 11, ......

LEts find out the difference

`-1-(-7)= 6`

`5-(-1)= 6`

`11 - 5=6`

So common difference is 6

General form of recursive for arithmetic sequence is

`a_(n)= a_(n-1) + d` where d is the common difference

we know common difference d= 6

a_n-1 is the previous term , an is the next term

Recursive formula is 4

`a_(n)= a_(n-1) + 6`

Answer 2

The common difference is -1-(-7) = 6. Since each term is 6 more than the last, the sequence is described by
a(1) = -7
a(n) = a(n-1) + 6 . . . n ≥ 2