7th term of the sequence -2-10-5-2- is -

The correct option is B 125√(2) Given sequence is nbsp;√(2),√(10),√(50),......... This sequence is a GP with common ratio r = nbsp;√(10)/√(2) =5√(2)/√(1)0 ...

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Byju's Answer

Standard X

Mathematics

Nth Term of a GP

7th term of t...

Question

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

$125 \sqrt{10}$

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$25 \sqrt{2}$

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125

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$125 \sqrt{2}$

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Solution

The correct option is D
$125 \sqrt{2}$

Given sequence is $\sqrt{2}, \sqrt{10}, \sqrt{50}, . . . . . . . . .$

This sequence is a GP with common ratio
$r = \frac{\sqrt{10}}{\sqrt{2}} = \frac{5 \sqrt{2}}{\sqrt{1} 0} = \sqrt{5}$ and first term $a = \sqrt{2} .$

$Now, a_{7} = a r^{6} = \sqrt{2} (\sqrt{5})^{6} = \sqrt{2} (5)^{3} = 125 \sqrt{2} .$

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7th term of the sequence √2,√10,5√2,......... is ___.

The correct option is D 125√2 Given sequence is √2,√10,√50,......... This sequence is a GP with common ratio r=√10√2=5√2√10=√5 and first term a=√2. Now, a7=ar6=√2(√5)6 =√2(5)3=125√2.

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