Find the sum of first n terms of an AP whose nth term is (5 − 6n).

Let an be the nth term of the AP.

∴ an = 5 − 6n

Putting n = 1, we get

First term, a = a1 = 5 − 6 × 1 = −1

Putting n = 2, we get

a2 = 5 − 6 × 2 = −7

Let d be the common difference of the AP.

$\therefore d=a_{2}-a_{1}=-7-(-1)=-7+1=-6$

Sum of first n terms of the AP, Sn

$=\frac{n}{2}[2 \times(-1)+(n-1) \times(-6)] \quad\left\{S_{n}=\frac{n}{2}[2 a+(n-1) d]\right\}$

$=\frac{n}{2}(-2-6 n+6)$

$=n(2-3 n)$

$=2 n-3 n^{2}$

Putting n = 20, we get

$S_{20}=2 \times 20-3 \times 20^{2}=40-1200=-1160$