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Question
If the pth term of an AP is q and its qth term is p then show that its (p + q)th term is zero
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Solution
In the given AP, let the first be a and the common difference be d.
Then , Tn = a +(n-1) d
⇒Tp = a+(p-1) d = q ...............(1)
⇒Tq = a + (q-1) d = p ...........(2)
On subtracting (i) from (ii), we get:
(q-p) d= (p-q)
⇒ d= -1
Putting d = - 1 in (i), we get:
a= (p+q -1)
Thus ,a = (p+q -1) and d = -1
Now , T p+q = a + (p+q-1)d
= (p+q-1) +(p+q-1)(-1)
= (p+q-1)- (p+q-1) =0
Hence, the ( p+q)th term is 0 (zero).
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