Question

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

Answer 1

Answer:

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

Step-by-step 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

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