The 7^{th} term of the sequence sqrt{2}, sqrt | vedclass

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

Question

(D) The given sequence is $\sqrt{2}, \sqrt{10}, 5\sqrt{2}, \dots$This is a Geometric Progression $(GP)$ where the first term $a = \sqrt{2}$.The common

Vedclass · Accepted Answer

$125\sqrt{2}$

Vedclass · Answer

(D) The given sequence is $\sqrt{2}, \sqrt{10}, 5\sqrt{2}, \dots$This is a Geometric Progression $(GP)$ where the first term $a = \sqrt{2}$.The common ratio $r = \frac{\sqrt{10}}{\sqrt{2}} = \sqrt{5}$.The $n^{th}$ term of a $GP$ is given by $t_n = a \cdot r^{n-1}$.For the $7^{th}$ term $(n=7)$:$t_7 = \sqrt{2} \cdot (\sqrt{5})^{7-1}$$t_7 = \sqrt{2} \cdot (\sqrt{5})^6$$t_7 = \sqrt{2} \cdot (5)^3$$t_7 = 125\sqrt{2}$.

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

Similar Questions

If $a = \sum_{n=0}^\infty x^n$,$b = \sum_{n=0}^\infty y^n$,and $c = \sum_{n=0}^\infty (xy)^n$,where $|x|, |y| < 1$,then which of the following is true?

If $p, q, r$ are in a geometric progression and $a, b, c$ are in another geometric progression,then $cp, bq, ar$ are in...

The numbers $(\sqrt{2} + 1), 1, (\sqrt{2} - 1)$ will be in

$A$ geometric progression consists of positive terms. If each term is equal to the sum of the next two terms,what is the common ratio of the progression?

The $G.M.$ of the numbers $3, 3^2, 3^3, ..., 3^n$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module