Question

If 3rd term of a G.P is 12 and 6th term is 96, find its 7th term.

• A. 288
• B. 192
• C. 182
• D. 144

Answer 1

The correct option is B

192

To find the $7^{th}$ term, we need the common ratio and the first term.

We will use the given two conditions to find them.

$T_3$ = 12

$\Rightarrow$ a $r^{3-1}$ = 12

a $r^2$ = 12------------(1)

$t_6$ = 96

$\Rightarrow$ a $r^{6-1}$ = 96

a$r^5$ = 96-------------(2)

$\frac{\left(2\right)}{\left(1\right)}$ $\Rightarrow$ $r^3$ = $\frac{96}{12}$

= 8

$\Rightarrow$
r = 2

a$r^2$ = 12

a × $2^2$ = 12

a = 3

$T_7$ = a$r^{7-1}$

= 3 $\times$ $2^6$

$=64\times 3$

= 192