Question

Find the sum of numbers between 1 to 140, divisible by 4

Answer 1

The numbers between 1 to 140 divisible by 4 are

4, 8, 12, ......, 136

The above sequence is an A.P.

∴ a = 4, d = 8 - 4 = 4

Let the number of terms in the A.P. be n.

Then, t_n = 136

Since t_n = a + (n – 1)d,

136 = 4 + (n – 1)(4)

∴ 136 = 4 + 4n – 4

∴ 136 = 4n

∴ n = `136/4`  = 34

Now, S_n = `"n"/2 ("t"_1 + "t"_"n")`

∴ S₃₄ = `34/2 (4 + 136)`

= 17(140)

= 2380

∴ The sum of numbers between 1 to 140, which are divisible by 4 is 2380.