In an A.P., the sum of first a terms is X & sum of first 2a terms is Y. If X = 3Y/4, find the sum of the first 3a terms of the A.P.
Explanation:
Sum of first a terms is X Sum of first 2a terms is Y
∴ Out of first 2a terms, sum of last a terms = Y - X
Now, out of first 3a terms, sum of first a terms is X sum of middle a terms is Y - X let sum of last a terms be S
⇒ sum of last a terms - sum of middle a terms = sum of middle a terms - sum of first a terms ⇒ S - (Y - X) = (Y - X) - X ⇒ S = 2Y - 3X
∴ Sum of all 3 a terms = X + (Y - X) + (2Y - 3X) = 3Y - 3X = 4X - 3X = X [Y = 4X/3]
Hence, option (c).
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