Question

Find the 12th term of a G.P whose 8th term is 192 and common ratio is 2​

Answer 1

hope it will help you

Answer 2

$\huge \boxed{ \underline{ \underline{ \bf{Answer}}}}$

$\underline{ \bf{Given :}}$

${8}^{th}$ term$({a}_{8})$ = 192.

Common ratio (r) = 2

$\underline{ \bf{To \: find \: :}}$

${12}^{th}$ term of the G.P

$\underline{ \bf{Process :}}$

$\implies \: a_{n} \: = \: a {r}^{n - 1}$

$\implies \: a_{8} \: = \: a {r}^{8- 1}$

$\implies \: a_{8} \: = \: a {r}^{7}$

$\implies \: 192 = a {(2)}^{7}$

$\implies \: a \: = \: \frac{192}{({2})^{7}} \: \: \: \: \: \: \: \: \: \rightarrow(1)$

Now,

$a_{12} \: = \: a ({ r})^{12 - 1}$

$a_{12} \: = \: a ({ r})^{11}$

$\: \: \: \: \: \: \: = \: \frac{192}{ {(2)}^{7} } \times {(2)}^{11}$ (from 1)

$\: \: \: \: \: \: \: = \:192 \: \times \: {(2)}^{11 - 7}$

$\: \: \: \: \: \: \: = \: 192 \: \times \: {(2)}^{4}$

$\: \: \: \: \: \: \: = \: 192 \: \times \: 16$

$\: \: \: \: \: \: \: = \: 3072$

$\boxed{\therefore \: \bf{{12}^{th} \: term \: = \: 3072 \: }}$