General GP determined by two terms for JEE

Formula

\(r=\left(\frac{a_q}{a_p}\right)^{\!\frac{1}{q-p}},\quad a=\frac{a_p}{r^{p-1}}\)

Variables: \(a\): first term, \(r\): common ratio, \(a_p,a_q\): pth and qth terms.

Conditions: For a GP with \(p\ne q\), with ratio defined appropriately in the real domain.

Reconstructing a GP from two given terms.