Find the sums indicated below:

25 + 21 + 17 + 13 + …… + (–51)

Formula used.

S_n = [2a + (n–1)d]

d = a_{n + 1}–a_n

In the sum above A.P follows

Is 25, 21, 17, 13, ……, (–51)

In the following A.P

⇒ a = 25,

⇒ d = 21–25 = –4

As the last term is –51

a_n = a + (n–1)d

–51 = 25 + (n–1)(–4)

–51 = 25–4n + 4

4n = 80

⇒ n = = 20

S_n = [2a + (n–1)d]

= [2×25 + (20–1)(–4)]

= 10[50 + 19×(–4)]

= 10[50–76]

= –260