The difference between the fourth term and th | vedclass

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

Question

(C) Let the terms of the $G.P.$ be $a, ar, ar^2, ar^3, ar^4, ar^5$,where $a$ is the first term and $r$ is the common ratio.According to the given cond

Vedclass · Accepted Answer

$728$

Vedclass · Answer

(C) Let the terms of the $G.P.$ be $a, ar, ar^2, ar^3, ar^4, ar^5$,where $a$ is the first term and $r$ is the common ratio.According to the given conditions:$ar^3 - a = 52 \Rightarrow a(r^3 - 1) = 52 \quad ......(1)$$a + ar + ar^2 = 26 \Rightarrow a(1 + r + r^2) = 26 \quad ......(2)$We know that $r^3 - 1 = (r - 1)(r^2 + r + 1)$.Dividing equation $(1)$ by equation $(2)$:$\frac{a(r - 1)(r^2 + r + 1)}{a(1 + r + r^2)} = \frac{52}{26}$$r - 1 = 2 \Rightarrow r = 3$.Substituting $r = 3$ in equation $(2)$:$a(1 + 3 + 9) = 26$ $\Rightarrow 13a = 26$ $\Rightarrow a = 2$.The sum of the first six terms is $S_6 = a(1 + r + r^2 + r^3 + r^4 + r^5) = a(1 + r + r^2)(1 + r^3)$.$S_6 = 26 	imes (1 + 3^3) = 26 	imes (1 + 27) = 26 	imes 28 = 728$.

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

Similar Questions

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

The sum of an infinite geometric series is $20$,and the sum of the squares of its terms is $100$. Find the common ratio of the geometric series.

The sum of the first four terms of a geometric progression $(G.P.)$ is $\frac{65}{12}$ and the sum of their respective reciprocals is $\frac{65}{18}$. If the product of the first three terms of the $G.P.$ is $1$,and the third term is $\alpha$,then $2\alpha$ is ....... .

If $1+\sin x+\sin ^{2} x+\ldots$ up to $\infty = 4+2 \sqrt{3}$,where $0 < x < \pi$ and $x \neq \frac{\pi}{2}$,then $x$ is equal to

If $a^2 + b^2 + 16c^2 = 2(3ab + 6bc + 4ac)$,where $a, b, c$ are non-zero numbers,then $a, b, c$ are in:

Vedclass Test Series

Exam Paper Generator

Online Exam Module