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:

$a_1 =-28$

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

$a_3 = a_2 + d = a_1+2d = -28-4\times2 = -36$

$a_4 = a_3 + d = a_1+3d = -28-4\times3 = -40$

and so on, up the n-th term

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