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.
