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.