In an AP, the pth term isqand (p+q)th term is 0. Show that its qth term isp.
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=0⇒q+qd=0∵a+(p-1)d=q⇒qd=-q⇒d=-1
Now, from equation. (1)
⇒a+(p-1)d=q⇒a+(p-1)×-1=q∵d=-1⇒a-p+1=q⇒a=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.