ICSE Class 10 Answered
if the sum of P terms of an arithmetic progression is equal to some of its Q terms. prove that the sum if(P+Q) terms of it is equal to zero
Asked by suneelmsc | 26 Apr, 2020, 19:49: PM
Expert Answer
Given: Sum of p terms of an AP = Sum of q terms of an AP
Sp=Sq
p/2[2a +(p-1)d]=q/2 [2a+(q-1)d]
p[2a +pd - d]=q[2a+qd - d ]
2ap + p2d - pd = 2aq + q2d - qd
2ap - 2aq + p2d - q2d - pd + qd = 0
2a(p-q) + (p+q)(p-q)d - d(p-q) = 0
(p-q)[2a + (p+q)d - d ]=0
(p-q)/2[2a + (p+q)d - d ]=0
Hence, the sum of its first (p+q) terms is 0.
Answered by Renu Varma | 26 Apr, 2020, 21:10: PM
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