Find the sum of all numbers from 1 to 140 which are divisible by 4.

4. Find the sum of all numbers from 1 to 140 which are divisible by 4.

Sol. 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.