Question

If $3^{rd}$ term of a G.P is 36 and $5^{th}$ term is 324, find its Common Ratio (r > 0)

• A. r=4
• B. r=8
• C. r=3
• D. r=9

Answer 1

The correct option is C

r=3

To find the $5^{th}$ term, we need the common ratio and the first term.

$t_n=a\times r^{(n-1)}$

$t_3$ = 36

$\Rightarrow$ $a{r}^{3-1}$ = 36

$a{r}^2$ = 36------------(1)

$t_5$ = 324

$\Rightarrow$ $a{r}^{5-1}$ = 324

$a{r}^4$ = 324-------------(2)
Divide (2) by (1)
$\Rightarrow$ $\frac{a{r}^5}{a{r}^2}$ = $\frac{r^4}{r^2}$ = $r^2$ = $\frac{324}{36}$

$r^2$ = 9

$r$ = +3 or -3
As it is given that $r$ > 0, $r$ = +3