Question

What is the recursive formula for this arithmetic sequence? -16,-7,2,11...

Answer 1

f(n)=-16
f(n)=f(n-1)+9

Answer 2

The recursive formula for the arithmetic sequence is given by:

`a_n = a_(n-1) +d` for
`n\geq 2`

where, d is the common difference.

Given the sequence:

-16,-7,2,11...

This is a arithmetic sequence:

`a_1 = -16` and d = 9

Since,

-7-(-16) = -7+6 = 9,

2-(-7) = 2+7 = 9,

11-2 = 9 and so on...

⇒ common difference(d) = 9

Substitute in [1] we have;

`a_n = a_(n-1)+9` for
`n\geq 2`

Therefore, the recursive formula for this arithmetic sequence is,

`a_1 = -16`

`a_n = a_(n-1)+9` for
`n\geq 2`