7^ th term of the sequence 2 , ;10 , ;5 2 , ;....... is - Vidyadip

MCQ

${7^{th}}$ term of the sequence $\sqrt 2 ,\;\sqrt {10} ,\;5\sqrt 2 ,\;.......$ is

A
$125\sqrt {10} $
B
$25\sqrt 2 $
C
$125$
✓
$125\sqrt 2 $

✓

Answer

Correct option: D.

$125\sqrt 2 $

d
(d) Given sequence is $\sqrt 2 ,\;\sqrt {10} ,\;\sqrt {50} ........$

Common ratio $r = \sqrt 5 $,

first term $a = \sqrt 2 $, then ${7^{th}}$ term

${t_7} = \sqrt 2 {(\sqrt 5 )^{7 - 1}} = \sqrt 2 {(\sqrt 5 )^6}$

$= \sqrt 2 {(5)^3} = 125\sqrt 2 $.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

$\int_{}^{} {\frac{{dx}}{{\sqrt {{x^2} - {a^2}} }}} $ equals

$\int {\frac{{dx}}{{{{\cos }^3}x\sqrt {2\sin 2x} }}} $ is equal to

Let the sum of the maximum and the minimum values of the function $f(x)=\frac{2 x^2-3 x+8}{2 x^2+3 x+8}$ be $\frac{ m }{ n }$ where $\text{gcd} (m, n) = 1.$ Then $m + n$ is equal to:

The value of $\sin 10^\circ + \sin 20^\circ + \sin 30^\circ + ... + $ $\sin 360^\circ $ is

Let $\vec{a}=2 \hat{i}+7 \hat{j}-\hat{k}, \vec{b}=3 \hat{i}+5 \hat{k}$ and $\vec{c}=\hat{i}-\hat{j}+2 \hat{k}$ Let $\vec{d}$ be a vector which is perpendicular to both $\overrightarrow{ a }$ and $\overrightarrow{ b }, \quad$ and $\quad \overrightarrow{ c } \cdot \overrightarrow{ d }=12$. Then $(-\hat{i}+\hat{j}-\hat{k}) \cdot(\vec{c} \times \vec{d})$ is equal to $........$.

Let $f$ : $A \to B$ be a function defined as $f(x)\, = \frac{{x - 1}}{{x - 2}}$ , where $A\, = R - \{2\}$ and $B\, = R - \{1\}$ . Then $f$ is

Let a straight line L pass through the point $P (2,-1,3)$ and be perpendicular to the lines $\frac{x-1}{2}=\frac{y+1}{1}=\frac{z-3}{-2}$ and $\frac{x-3}{1}=\frac{y-2}{3}=\frac{z+2}{4}$. If the line L intersects the yz -plane at the point Q , then the distance between the points P and Q is :

Let $N_1=2^{55}+1$ and $N_2=165$.Then

Let $\alpha$ be the constant term in the binomial expansion of $\left(\sqrt{ x }-\frac{6}{ x ^{\frac{3}{2}}}\right)^{ n }, n \leq 15$. If the sum of the coefficients of the remaining terms in the expansion is $649$ and the coefficient of $x^{-n}$ is $\lambda \alpha$, then $\lambda$ is equal to $..........$.

$\tan \left( {2{{\cos }^{ - 1}}\frac{3}{5}} \right) = $