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Question

Very-Short and Short-Answer Questions

If the sum of first p terms of an AP is (ap2 + bp), find its common difference. [CBSE 2010]

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Solution

Let Sp denotes the sum of first p terms of the AP.
Sp=ap2+bpSp-1=ap-12+bp-1 =ap2-2p+1+bp-1 =ap2-2a-bp+a-b
Now,
pth term of the AP, ap = Sp − Sp − 1
=ap2+bp-ap2-2a-bp+a-b=ap2+bp-ap2+2a-bp-a-b=2ap-a-b

Let d be the common difference of the AP.
d=ap-ap-1 =2ap-a-b-2ap-1-a-b =2ap-a-b-2ap-1+a-b =2a

Hence, the common difference of the AP is 2a.

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