Question

The product of $2^{\text{nd}}$ term and $4^{\text{th}}$ term of a G.P is 57600. If its $1^{st}$ term is 60, then find the G.P..

• A. 60, 180, 540...
• B. 60, 240, 960...
• C. 60, 120, 240,...
• D. 60, 300, 1800,...

Answer 1

The correct option is C

60, 120, 240,...

Given, $2^{\text{nd}}\text{term}\times 4^{\text{th}}\text{term}=57600.$
The $n^{\text{th}}$ term of a GP of first term $A$ and common ratio $r$ is given by
$a_n=a{r}^{n-1}.$
$\therefore ar\times a{r}^3=57600$
$\Rightarrow a^2{r}^4=57600$
$\Rightarrow (60{)}^2{r}^4=57600$ [Given: $a=60$]
$\Rightarrow r^4=\frac{57600}{3600}$
$\Rightarrow r^4=16$
$\Rightarrow r^4=2^4$
$\Rightarrow r=2$

$\therefore$ The Progression is $a,ar,a{r}^2,..=60,60\times 2,60\times 2^2....=60,120,\mathrm{240....}$