Question

Write an explicit formula for the sequence -13,-6,1,8

Answer 1

`\large\boxed{a_n=7n-20}`

Explanation:

It's an arithmetic sequence.

`-6-(-13)=-6+13=7\\1-(-6)=1+6=7\\8-1=7`

The difference is constant.

The explicit formula of an arihmetic sequence:

`a_n=a_1+(n-1)d`

Substitute:

`a_1=-13,\ d=7`

`a_n=-13+(n-1)(7)` use distributive property

`a_n=-13+7n-7\\\\a_n=7n+(-13-7)\\\\a_n=7n-20`