Find the sums indicated below:

7 + 12 + 17 + 22 + …… + 102

Formula used.

S_n = [2a + (n–1)d]

d = a_{n + 1}–a_n

In the sum above A.P follows

Is 7, 12, 17, 22, ……, 102

In the following A.P

⇒ a = 7,

⇒ d = 12–7 = 5

As the last term is 102

a_n = a + (n–1)d

102 = 7 + (n–1)5

102 = 7 + 5n–5

5n = 102–2

⇒ n = = 20

S_n = [2a + (n–1)d]

= [2×7 + (20–1)5]

= 10[14 + 19×5]

= 10[14 + 95]

= 1090