Question

In a GP , a8 = 192 , r = 2 then a12 = ....….......

Answer 1

EXPLANATION.

$\sf : \implies \: nth \: terms \: of \: a \: gp \\ \\ \sf : \implies \: a_{n} \: = ar {}^{n - 1} \\ \\ \sf : \implies \: a_{8} = a {r}^{7} \\ \\ \sf : \implies \: a {r}^{7} = 192 \\ \\ \sf : \implies \: a(2) {}^{7} = 192$

$\sf : \implies \: 128a = 192 \\ \\\sf : \implies \: a \: = \frac{192}{128} \\ \\ \sf : \implies \: a \: = \frac{3}{2}$

$\sf : \implies \: a_{12} \: = a {r}^{11} \\ \\ \sf : \implies \: ( \frac{3}{2}) \times (2) {}^{11} \\ \\ \sf : \implies \: 3 \times (2) {}^{10} = 3072$