Sum of nth term of a G.P = Sn = \(\frac{ar^n - 1}{r - 1}\) sum of the first two terms = \(\frac{ar^2 - 1}{r - 1}\) x = a(r + 1) sum of the last two terms = Sn - Sn - 2 = \(\frac{ar^n - 1}{r - 1}\) - \(\frac{(ar^{n - 1})}{r - 1}\) = \(\frac{a(r^n - 1 - r^{n - 2} + 1)}{r - 1}\) (r2 - 1) ∴ \(\frac{ar^{n - 2}(r + 1)(r - 1)}{1}\)= arn - 2(r + 1) = y = a(r + 1)r^n - 2 y = xrn - 2 = yrn - 2 \(\frac{y}{x}\) = r = (\(\frac{y}{x}\))\(\frac{1}{n - 2}\)