Question

Find the 20th term of a gp whose 8th term is 192 and coomon ratio is 192

Answer 1

Nth term of GP is ar power (n-1). Where a is the first term ,r is common ratio. Now first find a from 8th term then u will get 'a' .and now find the 20th term.

Answer 2

Answer:

As we have

$a_8=192 \\ </p><p>r=192</p><p>$

we have the formula to find nth term of an GP

as :-

$a_n= {ar}^{n - 1}$

As in this question we have to find the 20th term of the given GP whose 8th term is 192 and common ratio is also 192 .

We can find it by putting the values as :-

1) firstly we have to find the value of first term as:-

$a_8=192 \\ \implies \: a \times {r}^{7} = 192 \\ \implies \: a = \frac{192}{ {192}^{7} } \\ \implies \: a = \frac{1}{ {192}^{6} }$

Now ;

$a_{20}=a {r}^{20 - 1} \\ = \frac{1}{ {192}^{6} } \times {192}^{19 } \\ = {192}^{19 - 6 } \\ = {192}^{13} \: \: \: \: \: \: \: \: \boxed { \boxed{Answer}}$