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.