In a G.P., if the (m + n)th term is p and the (m – n)th term is q, then
the square of its mth term is
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given:
ar^(m+n-1)=p
and
ar^(m-n-1)=q
on multiplying them
ar^(m+n-1)* ar^(m-n-1)=p*q
a²*r^(m+n-1+m-n-1)=pq
a²*r^(2m-2)=pq
a²*r^2(m-1)=pq
(ar^(m-1))²=pq( answer)
ar^(m+n-1)=p
and
ar^(m-n-1)=q
on multiplying them
ar^(m+n-1)* ar^(m-n-1)=p*q
a²*r^(m+n-1+m-n-1)=pq
a²*r^(2m-2)=pq
a²*r^2(m-1)=pq
(ar^(m-1))²=pq( answer)
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