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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.