Find the sums indicated below:

(–100) + (–92) + (–84) + …… + 92

Formula used.

S_n = [2a + (n–1)d]

d = a_{n + 1}–a_n

In the sum above A.P follows

Is –100, –92, –84, ……, 92

In the following A.P

⇒ a = –100,

⇒ d = –92–(–100) = –92 + 100 = 8

As the last term is 92

a_n = a + (n–1)d

92 = –100 + (n–1)8

92 = –100 + 8n–8

8n = 92 + 108

⇒ n = = 25

S_n = [2a + (n–1)d]

= [2×(–100) + (25–1)8]

= [–200 + 24×8]

= [–200 + 192]

= –100