Question

If 3rd term of a G.P is 12 and 6th term is 96, then its 7th term will be _______.

Answer 1

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

$T_3$ = 12

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

$T_6$ = 96

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

On dividing equation (2) by equation (1), we get

$r^3$ = $\frac{96}{12}$

= 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