Question

What is the explicit formula for this sequence -7, -4, -1, 2, 5

Answer 1

Answer:

$\large\boxed{a_n=3n-10}$

Step-by-step explanation:

It's an arithmetic sequence.

$-4-(-7)=-4+7=3\\-1-(-4)=-1+4=3\\2-(-1)=2+1=3\\5-2=3$

The difference is constant.

The explicit formula of an arithmetic sequence:

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

Substitute:

$a_1=-7,\ d=3$

$a_n=-7+(n-1)(3)$          use distributive property

$a_n=-7+3n-3\\\\a_n=3n+(-7-3)\\\\a_n=3n-10$