The fifth of the H-P- 2-2 1-2- 3 1-3- - will be

The correct option is D 10 Series, 2,21/2,31/3,................. are in H.P. ⇒1/2,2/5,3/10,......... will be in A.P. Now first term a = 1/2 and common differen ...

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Standard XI

Mathematics

Geometric Progression

The fifth of ...

Question

The fifth of the H.P., 2,2$\frac{1}{2}$,3$\frac{1}{3}$,................. will be

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Solution

The correct option is D
10

Series, 2,2 $\frac{1}{2}$ ,3 $\frac{1}{3}$ ,................. 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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Similar questions

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The fifth of the H.P., 2,2\(\frac{1}{2}\),3\(\frac{1}{3}\),................. will be

The correct option is D 10 Series, 2,212,313,................. are in H.P. ⇒12,25,310,......... will be in A.P. Now first term a = 12 and common difference d = −110 So, 5th term of the A.P. = 12+(5−1)(−110) = 110 Hence 5th term in H.P. is 10.