Find the sum of n terms in the geometric prog | vedclass

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

Question

(A) The given $G.P.$ is $\sqrt{7}, \sqrt{21}, 3 \sqrt{7}, \ldots$Here,the first term $a = \sqrt{7}$ and the common ratio $r = \frac{\sqrt{21}}{\sqrt{7

Vedclass · Accepted Answer

$\frac{\sqrt{7}(\sqrt{3}+1)}{2}\left[(3)^{\frac{n}{2}}-1\right]$

Vedclass · Answer

(A) The given $G.P.$ is $\sqrt{7}, \sqrt{21}, 3 \sqrt{7}, \ldots$Here,the first term $a = \sqrt{7}$ and the common ratio $r = \frac{\sqrt{21}}{\sqrt{7}} = \sqrt{3}$.The sum of $n$ terms of a $G.P.$ is given by $S_{n} = \frac{a(r^{n}-1)}{r-1}$.Substituting the values,we get $S_{n} = \frac{\sqrt{7}((\sqrt{3})^{n}-1)}{\sqrt{3}-1}$.To rationalize the denominator,multiply the numerator and denominator by $(\sqrt{3}+1)$:$S_{n} = \frac{\sqrt{7}((\sqrt{3})^{n}-1)(\sqrt{3}+1)}{(\sqrt{3}-1)(\sqrt{3}+1)}$$S_{n} = \frac{\sqrt{7}(\sqrt{3}+1)(3^{\frac{n}{2}}-1)}{3-1}$$S_{n} = \frac{\sqrt{7}(\sqrt{3}+1)}{2}\left[(3)^{\frac{n}{2}}-1\right]$.

Find the sum of $n$ terms in the geometric progression $\sqrt{7}, \sqrt{21}, 3 \sqrt{7}, \ldots$

Similar Questions

The coefficient of $x^{49}$ in the expansion of $(x - 1)(x - \frac{1}{2})(x - \frac{1}{2^2}) \dots (x - \frac{1}{2^{49}})$ is equal to

Suppose four distinct positive numbers $a_1, a_2, a_3, a_4$ are in $G.P.$ Let $b_1=a_1, b_2=b_1+a_2, b_3=b_2+a_3$ and $b_4=b_3+a_4$.
$STATEMENT-1$ : The numbers $b_1, b_2, b_3, b_4$ are neither in $A.P.$ nor in $G.P.$
$STATEMENT-2$ : The numbers $b_1, b_2, b_3, b_4$ are in $H.P.$

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 $G.P.$

If $x > 1, y > 1, z > 1$ are in geometric progression,then in which progression are $\frac{1}{1 + \ln x}, \frac{1}{1 + \ln y}, \frac{1}{1 + \ln z}$?

If $a, b$ and $c$ form a geometric progression with common ratio $r$,then the sum of the ordinates of the points of intersection of the line $ax + by + c = 0$ and the curve $x + 2y^2 = 0$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module