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Question

In an AP, the pth term isqand (p+q)th term is 0. Show that its qth term isp.


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Solution

Find the qth term of the AP

Given, pth term is qand (p+q)th term is 0.

Let, First term=a and Common difference of the given A.P.=d

a+(p-1)d=q......(1)

and a+(p+q-1)d=0

a+(p-1)d+qd=0q+qd=0a+(p-1)d=qqd=-qd=-1

Now, from equation. (1)

a+(p-1)d=qa+(p-1)×-1=qd=-1a-p+1=qa=p+q-1

qth term =a+(q-1)d

=p+q-1+(q-1)×(-1)a=p+q-1andd=-1=p+q-1-q+1=p

Hence, the qth term of the given AP isp.


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