if pth term is q and qth is p .find (pq)th term is 1
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let a is the first term and d is the common difference of given AP
now,
pth term=a+(p-1) d
q=a+(p-1) d --------------(1)
qth term =a+(q-1) d
p=a+(q-1) d --------------------(2)
solve equation (1) and (2)
q-(p-1) d=p-(q-1) d
(q-1-p+1) d=p-q
d=-1
and a =q+p-1
so,
(pq)th term=a+(pq-1) d
=p+q-1-pq+1
=p + q -pq
now,
pth term=a+(p-1) d
q=a+(p-1) d --------------(1)
qth term =a+(q-1) d
p=a+(q-1) d --------------------(2)
solve equation (1) and (2)
q-(p-1) d=p-(q-1) d
(q-1-p+1) d=p-q
d=-1
and a =q+p-1
so,
(pq)th term=a+(pq-1) d
=p+q-1-pq+1
=p + q -pq
abhi178:
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