The first term of a H P whose second term is 52 and third term is 103- is

Let x be the first term of H.P. x, 52, 103 are in H.P. ⇒ 1x, 25, 310 are in A.P. So, nbsp; 25 1x =310 25 1x=310 45 1x=12 x = 2 So, the first term = 2 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

nth Term of HP

The first ter...

Question

The first term of a H P whose second term is $\frac{5}{2}$ and third term is $\frac{10}{3}$ , is___

Open in App

Solution

Let $x$ be the first term of H.P.

$x, \frac{5}{2}, \frac{10}{3}$ are in H.P.

$\Rightarrow$ $\frac{1}{x}, \frac{2}{5}, \frac{3}{10}$ are in A.P.

So, $\frac{2}{5} - \frac{1}{x} = \frac{3}{10} - \frac{2}{5}$

$- \frac{1}{x} = \frac{3}{10} - \frac{4}{5}$

$\frac{1}{x} = \frac{1}{2}$

$x = 2$

So, the first term = 2

Suggest Corrections

Similar questions

Q. If the first, second and the fourth terms of a perpendicular are

5, 3

and

15

respectively is third terms.

Q. Q. The sum of the first 16 terms of an AP whose first term and third term are 5 and 15 respectively is

Q. The

21^{s t}

term of the AP whose first term is

3

and second term is

4

, is

Q. The first, second and third term of a proportion are

\frac{1}{3}, \frac{1}{6} and \frac{2}{5} respectively

.
What is the fourth term?

Find the sum of first 20 terms of an A. P. whose first term is 3 and the last term is 57.

Join BYJU'S Learning Program

The first term of a H P whose second term is 52 and third term is 103, is___

Let x be the first term of H.P. x,52,103 are in H.P. ⇒ 1x,25,310 are in A.P. So, 25−1x=310−25 −1x=310−45 1x=12 x=2 So, the first term = 2

The first term of a H P whose second term is $\frac{5}{2}$ and third term is $\frac{10}{3}$ , is___