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Question: Answered & Verified by Expert
$7^{\text {th }}$ term of the sequence $\sqrt{2}, \sqrt{10}, 5 \sqrt{2}, \ldots \ldots$ is
MathematicsSequences and SeriesJEE Main
Options:
  • A $125 \sqrt{10}$
  • B $25 \sqrt{2}$
  • C $125$
  • D $125 \sqrt{2}$
Solution:
1431 Upvotes Verified Answer
The correct answer is: $125 \sqrt{2}$
Given sequence is $\sqrt{2}, \sqrt{10}, \sqrt{50} \ldots \ldots$ Common ratio $r=\sqrt{5}$, first term $a=\sqrt{2}$, then $7^{\text {th }}$ term
$t_7=\sqrt{2}(\sqrt{5})^{7-1}=\sqrt{2}(\sqrt{5})^6=\sqrt{2}(5)^3=125 \sqrt{2}$

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