Find the sums indicated below:

5 + 10 + 15 + …… + 100

Formula used.

S_n = [2a + (n–1)d]

d = a_{n + 1}–a_n

In the sum above A.P follows

Is 5, 10, 15, ……, 100

In the following A.P

⇒ a = 5,

⇒ d = 10–5 = 5

As the last term is 100

a_n = a + (n–1)d

100 = 5 + (n–1)5

100 = 5 + 5n–5

5n = 100

⇒ n = = 20

S_n = [2a + (n–1)d]

= [2×5 + (20–1)5]

= 10[10 + 19×5]

= 10[10 + 95]

= 1050