Let the first three terms of G.P. be $\frac{a}{r}$ , a , ar , where a is the first term and r is the common ratio. Then $\frac{a}{r}$ + a + ar = $\frac{39}{10}$ and $\frac{a}{r}$ × a × ar = 1 ⇒ $a\left(\frac{1}{r}+1+1\right)$ = $\frac{39}{10}$ and $a^3$ = 1 ⇒ a = 1 ∴ $1\left(\frac{1}{r}+1+r\right)$ = $\frac{39}{10}$ ⇒ 10 (1 + r + $r^2$) = 39r ⇒ $10r^2$ – 29r + 10 = 0 ⇒ $10r^2$ – 25r – 4r + 10 = 0 ⇒ (5r – 2) (2r – 5) = 0 ⇒ r = $\frac{2}{5},\frac{5}{2}$ (i) When r = $\frac{5}{2}$ , the terms are $\frac{2}{5},1,\frac{5}{2}$ (ii) When r = $\frac{2}{5}$ , then terms are $\frac{5}{2},1,\frac{2}{5}$