Question

Please help!! I’ve been stuck on this for days!!! Finding the common difference and equation for the following arithmetic sequence! Thanks

Answer 1

The common difference is d = -4, since

-32 - (-28) = -4

-36 - (-32) = -4

-40 - (-36) = -4

and so on.

In the arithmetic sequence starting with
`a_1=-28` and common difference -4, the next term is obtained by adding -4 to the previous one:

`a_1 =-28`

`a_2 = a_1 + d = -28 - 4 = -32`

`a_3 = a_2 + d = a_1+2d = -28-4*2 = -36`

`a_4 = a_3 + d = a_1+3d = -28-4*3 = -40`

and so on, up the n-th term

`a_n = a_(n-1)+d = a_1+(n-1)d = \boxed{-28-4(n-1)}`