Question

If the sum of three terms of G.P. is 19 and product is 216, then the common ratio of the series is
[Roorkee 1972]

• A. $-\frac{3}{2}$
• B. $\frac{3}{2}$
• C. 2
• D. 3

Answer 1

The correct option is B $\frac{3}{2}$

Let three terms of G.P. are $a,ar,a{r}^2.$ Then
$a+ar+a{r}^2=19\Rightarrow a[1+r+r^2]=19$ …..(i)
$a.ar.a{r}^2=216\Rightarrow a^3{r}^3=216\Rightarrow ar=6$ …..(ii)
Dividing (ii) by (i),

$\frac{6}{r}+\frac{6}{r}r+\frac{6}{r}{r}^2=19\Rightarrow \frac{6}{r}+6+6r=19$

$\Rightarrow r^2-\frac{13}{6}r+1=0.$ Hence $r=\frac{3}{2}.$