[administration]

Q. In a GP the (p+q)th term is m. (p-q)th term is n. Find the pth and qth term of the series?

[Wonder Boy]

Let 1st term and common ratio of GP be a & r respectively.

so m = a.r^p+q-1

and n = a.r^p-q-1

mn= a²r^2p-2 — > ar^p-1 = (mn)^1/2 = pth term

m/n = r^p+q-1-p+q+1 –> m/n = r^2q –> r = (m/n)^1/2q

Now ar^p+q-1=m –> ar^q-1.r^p = m –> ar^q-1 =mr^-p = qth term

so qth term = mr^-p = m(m/n)^-p/2q = m^1-p/2qn^p/2q

[Author]

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