Question

Find the sum of all numbers from 1 to 140
Which are divisibly by 4.​

Answer 1

Step-by-step explanation:

The natural numbers from 1 to 140 that are divisible by 4 are as follows : 4, 8, 12, 16, .............., 140

These numbers from an A.P. with a = 4, d = 4

Let, 140 be the nth term of A.P.

∴ tn = 140

tn = a + (n – 1) d

∴ 140 = 4 + (n – 1) 4

∴ 140 = 4 + 4n – 4

∴ 140 = 4n

∴ n = 140/4

∴ n = 35

∴ 140 is 35 term of A.P.

Now, We have to find sum of 35 terms i.e. S35,

Sn = n/2[2a + (n – 1)d]

∴ S35 = 35/2 [2 (4) + (35 – 1) 4]

∴ S35 = 35/2[8 + 34 (4)]

∴ S35 = 35/2 [8 + 136)

∴ S35 = 35/2 [144]

∴ S35 = 2520

∴ Sum of natural numbers from 1 to 140 that are divisible by 4 is 2520.