Question

Find the explicit formula for the arithmetic sequence -2,-14,-26,-38

Answer 1

Answer:

$\large\boxed{a_n=10-12n}$

Step-by-step explanation:

It's an arithmetic sequence.

$-14-(-2)=-14+2=-12\\-26-(-14)=-26+14=-12\\-38-(-26)=-38+26=-12$

The difference is constant.

The explicit formula of an arithmetic sequence:

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

Substitute:

$a_1=-2,\ d=-12$

$a_n=-2+(n-1)(-12)$        use distributive property

$a_n=-2-12n+12\\\\a_n=(-2+12)-12n\\\\a_n=10-12n$