The sum of first 'n' terms. Sn of a particular Arithmetic Progression is given by Sn=12n - 2n^2. Find the first term and the common difference

Let a be the first term and d the common difference between consecutive terms. Then the next few terms in the sequence are

a + d

a + 2d

a + 3d

and so on, up to the k-th term

a + (k - 1) d

The sum of the first n terms of this sequence is

Expanding the sum, we have

It follows that

a - d/2 = 12

d/2 = -2

Solve these equations for a and d.

d/2 = -2   ==>   d = -4

a - d/2 = a + 2 = 12   ==>   a = 10

So the sequence is

10, 6, 2, -2, -6, -10, -14, …

answer: i don't understand it

step-by-step explanation: sorry