If the 2^{text{nd}} and 5^{text{th}} terms of | vedclass

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

Question

(A) Given that,$T_{2} = 24$ and $T_{5} = 3$.In a $G$.$P$.,the $n^{	ext{th}}$ term is given by $T_{n} = ar^{n-1}$.So,$ar = 24$ $(1)$ and $ar^{4} = 3$

Vedclass · Accepted Answer

$ \frac{189}{2} $

Vedclass · Answer

(A) Given that,$T_{2} = 24$ and $T_{5} = 3$.In a $G$.$P$.,the $n^{	ext{th}}$ term is given by $T_{n} = ar^{n-1}$.So,$ar = 24$ $(1)$ and $ar^{4} = 3$ $(2)$.Dividing equation $(2)$ by equation $(1)$,we get $\frac{ar^{4}}{ar} = \frac{3}{24}$ $\Rightarrow r^{3} = \frac{1}{8}$ $\Rightarrow r = \frac{1}{2}$.Substituting $r = \frac{1}{2}$ in equation $(1)$,we get $a 	imes \frac{1}{2} = 24 \Rightarrow a = 48$.The sum of the first $n$ terms of a $G$.$P$. is $S_{n} = \frac{a(1-r^{n})}{1-r}$.For $n = 6$,$S_{6} = \frac{48(1-(1/2)^{6})}{1-1/2} = \frac{48(1-1/64)}{1/2} = 96 	imes \frac{63}{64} = \frac{3 	imes 63}{2} = \frac{189}{2}$.

If the $2^{\text{nd}}$ and $5^{\text{th}}$ terms of a $G$.$P$. are $24$ and $3$ respectively,then the sum of the $1^{\text{st}}$ six terms is:

Similar Questions

The difference between the fourth term and the first term of a Geometric Progression is $52$. If the sum of its first three terms is $26$,then the sum of the first six terms of the progression is

The third term of a $G$.$P$. is $9$. The product of its first five terms is

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:

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 $x, y, z$ are in geometric progression and $a^x = b^y = c^z$,then . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module