Question

find the 12th term of a G.p whose 8th term is 192 and commo ratio is 2

Answer 1

Now for 12th term

ar^11 = 192/128*2^11
= 3072

Thanks

Answer 2

Hey !

In an GP, the n th term can be given as : $ar^{ n - 1 }$. 

a = First term of the GP

r = Common Ratio

n = Number of terms

Given : 8th term = 192

=> $ar^{8-1} = 192$

Given that r = 2. Hence substituting in the equation we get,

=> $a * 2^{7} = 192$

=> $a * 128 = 192$

=> a = 192 / 128

=> a = 3 / 2

Therefore First term of the GP = 3 / 2 and common ratio = 2

Therefore 12 th term = $a_{12} = ar^{12 - 1 }$

=> $ar^{11} = \frac{3}{2} * 2^{11}$

=> ar¹¹ = 3 * 2¹⁰

=> ar¹¹ = 1024 * 3 

=. ar¹¹ = 3072.

Hence the required 12 th term is 3072.

Hope helped :-)