Question

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

Answer 1

10-12n

Explanation:

Answer 2

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

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`