The fifth of the H-P- 2-5-2-10-3- will be

Series, 2,5/2,10/3,................. are in H.P. ⇒1/2,2/5,3/10,......... will be in A.P. Now first term a = 1/2 and common difference d = 1/10 So, 5^th term ...

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The fifth of ...

Question

The fifth of the H.P. 2, $\frac{5}{2}$ , $\frac{10}{3}$ ,................. will be

$5 \frac{1}{5}$

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$\frac{1}{10}$

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$3 \frac{1}{5}$

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Solution

The correct option is B
10

Series, 2, $\frac{5}{2}$ , $\frac{10}{3}$ ,................. are in H.P. $\Rightarrow \frac{1}{2}, \frac{2}{5}, \frac{3}{10}$ ,......... will be in A.P.

Now first term a = $\frac{1}{2}$ and common difference d = $- \frac{1}{10}$

So, $5^{t h}$ term of the A.P. = $\frac{1}{2} + (5 - 1) (- \frac{1}{10})$ = $\frac{1}{10}$

Hence $5^{t h}$ term in H.P. is 10.

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