Question

find its 8th termof GP

Answer 1

Hey there!!

Here's your answer..

We know that the general term in a G.P is given by $a r^{n-1}$

It is given that the sixth term is 192

⇒ n = 6 and $a r^{6-1} = a r^{5}$ = 192

Also, given that 10th term is 3072

⇒ n = 10 and $a r^{10-1} = a r^{9}$ = 3072

Now, let us divide $a r^{9}$ by $a r^{5}$

⇒ [tex] \frac{a r^{9} }{a r^{5} } = \frac{3072}{192} [/tex]

⇒ $r^{4} = \frac{3072}{192}$

⇒ $r^{4} = 16 = 2^{4}$

⇒ r = 2 

Now, substituting r = 2 in $a r^{5} = 192$, we get,

$a .2^{5} = 192$

⇒ a = $\frac{192}{ 2^{5} } = \frac{192}{32} = 6$

Now, we got the result as a = 6 and r = 2

We need the 8th term

⇒ n = 8 and $a r^{8-1} = a r^{7} = 6. 2^{7} = 6.128 = 768$

So, the 8th term is 768

Hope it helps!!