Question

find the 12th term of a gp whose 8th term is 192 and the common ratio is 2

Answer 1

a + 7d = 192
d = 2

then a +7×2 = 192
a + 14 = 192
a = 192 -14
a = 178
then
a + 11d = 178 + 11 × 2
= 178 + 22
= 200 is the answer

Answer 2

$\large \underline{ \underline{ \sf \: Solution : \: \: \: }}$

Given ,

$\star \: \: \: \sf a {r}^{7} = 192 \\ \\ \star \: \: \: \sf r = 2$

So ,

$\implies \sf a {(2)}^{7} = 192 \\ \\ \implies \sf 128a = 192 \\ \\ \implies \sf a = \frac{192}{128} \: \: \sf or \: \: \frac{3}{2}$

Therefore , 12th term of the given GP is :

$\implies \sf a_{12} = a {(r)}^{11} \\ \\ \implies a_{12} = \sf (\frac{3}{2} ) \times{(2)}^{11} \\ \\ \implies a_{12} = \sf 3 \times {(2)}^{10} \\ \\\implies a_{12} = \sf 3 \times 1024 \\ \\\implies a_{12} = \sf 3072$

Hence , the required value is 3072