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If pth term of an AP …

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If pth term of an AP is q and qth term is p than prove that its (p+q)th term is zero.

Posted by Anushka Dixit 5 years, 5 months ago

Gaurav Seth 5 years, 5 months ago

Let a is the first term of AP and d is the common difference

p^th term = a + (p-1) d = q .................(1)

q^th term = a + (q-1) d = p .................(2)

By subtracting eqn(2) from eqn(1), we get d = -1

if we subsititue d = -1 in eqn.(1), we get a = p+q-1

n^th term = a+(n-1)d = (p+q-1) + (n-1)(-1) = p+q-n

(p+q)^th term = a+(p+q-1)d = (p+q-1)+(p+q-1)(-1) = 0

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