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

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(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

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$125\sqrt{2}$

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(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 $r$ is calculated as $r = \frac{\sqrt{10}}{\sqrt{2}} = \sqrt{5}$.The $n^{th}$ term of a $GP$ is given by the formula $t_n = a \cdot r^{n-1}$.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 = \sqrt{2} \cdot 125 = 125\sqrt{2}$.

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

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