Find the 12^{text{th}} term of a G.P. whose 8 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given: Common ratio,$r = 2$. Let $a$ be the first term of the $G.P.$ We know that the $n^{	ext{th}}$ term of a $G.P.$ is given by $a_n = a r^{n-1

Vedclass · Accepted Answer

$3072$

Vedclass · Answer

(A) Given: Common ratio,$r = 2$. Let $a$ be the first term of the $G.P.$ We know that the $n^{	ext{th}}$ term of a $G.P.$ is given by $a_n = a r^{n-1}$. Given $a_8 = 192$,we have $a r^7 = 192$. Substituting $r = 2$: $a(2)^7 = 192$. $a(128) = 192$. $a = \frac{192}{128} = \frac{3}{2}$. Now,find the $12^{	ext{th}}$ term: $a_{12} = a r^{11}$. $a_{12} = \left(\frac{3}{2}ight) 	imes (2)^{11} = 3 	imes 2^{10}$. $a_{12} = 3 	imes 1024 = 3072$.

Find the $12^{\text{th}}$ term of a $G.P.$ whose $8^{\text{th}}$ term is $192$ and the common ratio is $2$.

Similar Questions

Consider an infinite geometric series with first term $a$ and common ratio $r$. If its sum is $4$ and the second term is $3/4$,find the values of $a$ and $r$.

Find four numbers forming a geometric progression in which the third term is greater than the first term by $9,$ and the second term is greater than the $4^{\text{th}}$ term by $18.$

If the sum of $n$ terms of a $G.P.$ is $255$,the $n^{th}$ term is $128$,and the common ratio is $2$,then the first term will be:

The sum of the first three terms of a $G.P.$ is $16$ and the sum of the next three terms is $128$. Determine the first term,the common ratio,and the sum to $n$ terms of the $G.P.$

Find the $20^{\text{th}}$ and $n^{\text{th}}$ terms of the $G.P.$ $\frac{5}{2}, \frac{5}{4}, \frac{5}{8}, \dots$

Vedclass Test Series

Exam Paper Generator

Online Exam Module