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In an AP of which ‘a’ is the Ist term, if the sum of the Ist p terms is equal to zero , show that the sum of the next q terms is -a (p+ q) q/(p-1).
Asked by rushabhjain.avv | 20 Feb, 2019, 08:57: PM
Let d be the common difference in A.P.

If sum of p terms zero, then we have,  2a +(p-1)d = 0   or  2a+pd = d   and d = -2a/(p-1)  ...................(1)

sum S of next q terms,  S = (q/2)[ 2(a+pd) + (q-1)d ] = (q/2) [ 2a + pd +pd +(q-1)d ] = (q/2)[p+q]d = -a (p+q)  [ q/(p-1) ] .................(2)

It is to be noted that in eqn.(2) we have used 2a+pd = d and d = -2a/(p-1) as given in eqn.(1)
Answered by Thiyagarajan K | 21 Feb, 2019, 10:55: AM

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