Mathematics
If the sum of first p terms of an A.P. is ap2 + bp, then its common difference is :
a
3a + b
a + b
2a
AP
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Answer
Given,
⇒ Sp = ap2 + bp
⇒ Tp = Sp - Sp - 1
= ap2 + bp - [a(p - 1)2 + b(p - 1)]
= ap2 + bp - [a(p2 - 2p + 1) + bp - b]
= ap2 + bp - [ap2 - 2ap + a + bp - b]
= ap2 + bp - ap2 + 2ap - a - bp + b
= 2ap - a + b.
d = Tp - Tp - 1
= 2ap - a + b - [2a(p - 1) - a + b]
= 2ap - a + b - [2ap - 2a - a + b]
= 2ap - a + b - 2ap + 2a + a - b
= 2a.
Hence, option 4 is the correct option.
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