Question

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

Answer 1

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

⇒ a $r^{3-1}$ = 12

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

$T_6$ = 96

⇒ a $r^{6-1}$ = 96

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

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

= 8

⇒ r = 2

a$r^2$ = 12

a $\times 2^2$ = 12

a = 3

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

= 3 $\times 2^6$

= 64 $\times$ 3

= 192