Q1 of 36 Page 161

The first term of an A.P.is a, and the sum of the first p terms is zero, show that the sum of its next q terms is

[Hint: Required sum = Sp+q – Sp]


Given first term is ‘a’ and sum of first p terms is Sp = 0 we have to find the sum of next q terms


Total terms are p + q


So, sum of all terms minus the sum of the first p terms will give the sum of next q terms


But sum of first p terms is 0 hence sum of next q terms will be the same as sum of all terms


So, we have to find sum of p + q terms


Sum of n terms of AP is given by


Where a is first term and d is the common difference


Using the given hint


⇒ Required sum = Sp+q – Sp


Using Sn formula



Now we have to find d


We use the given Sp = 0 to find d



⇒ 0 = 2a + (p – 1) d



Put this value of d in (i)


⇒required sum







Hence proved.


More from this chapter

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2

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A man accepts a position with an initial salary of Rs 5200 per month. It is understood that he will receive an automatic increase of Rs 320 in the very next month and each month thereafter.

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 4

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5

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