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in Arithmetic Progression by (44.5k points)
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If the sum of n terms of an A.P. is n P + 1/2 n( n - 1)Q , where P and Q are constants, find the common difference of the A.P.

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Best answer

⇒ S1 = P

⇒ a1 = P

Taking n = 2, we get

⇒ S3 = 3P + 3Q

∴ a3 = S3 – S2 = 3P + 3Q – 2P – Q = P + 2Q

So, a = P,

d = a2 – a1 = P + Q – (P) = Q

= a3 – a2 = P + 2Q – (P + Q) = P + 2Q – P – Q = Q

Hence, the common difference is Q.

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