Find the sum of first 11 positive numbers which are multiples of 6.

3. Find the sum of first 11 positive numbers which are multiples of 6.

Sol. The positive integers which are divisible by 6 are 6, 12, 18, 24, ........

The number form an A.P. with a = 6, d = 6.

The sum of first 11 positive integers divisible by 6 is (S11)

Sn = n/2 [2a + (n – 1) d]
∴  S11 = 11/2 [2a + (11 – 1) d]
∴ S11 = 11/2 [2 (6) + 10 (6)]

∴ S11 = 11/2 [12 + 60]

∴ S11 = 11/2 (72)
∴ S11 = 11 × 36
S11 = 396
∴  Sum of first 11 positive integers which are divisible by 6 is 396.