Let $a_{1}, a_{2}, a_{3}, . . . . . . . . . . . . .$ be in harmonic progression with $a_{1} = 5 a n d a_{2} = 25.$ The least positive integer n for which $a_{n} < 0$ is

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D
25

If $a_{1}, a_{2}, a_{3}, . . . . . .$ are in harmonic progression, then $\frac{1}{a_{1}}, \frac{1}{a_{2}}, \frac{1}{a_{3}} . . . . .$ are in AP.
First term of AP, $\frac{1}{a_{1}} = \frac{1}{5}$
20th term of AP, $\frac{1}{a_{20}} = \frac{1}{25}$
$\Rightarrow \frac{1}{5} + 19 d = \frac{1}{25}$
$\Rightarrow d = \frac{- 4}{19 \times 25}$
We have to find the least positive integer n for which $a_{n} < 0$
$\Rightarrow \frac{1}{5} + (n - 1) d < 0$
$\Rightarrow \frac{1}{5} + (n - 1) (\frac{- 4}{19 \times 25}) < 0$
$\Rightarrow (n - 1) > \frac{95}{4}$
$\Rightarrow n > 24.75$

Suggest Corrections

Similar questions

Q. Let

a_{1}, a_{2}, a_{3} .

..... be in harmonic progression with

a_{1} = 5

and

a_{20} = 25

. The least positive integer n for which

a_{n} < 0

Q. Let

a_{1}, a_{2}, a_{3}, . . . . . . . . . . . . .

be in harmonic progression with

a_{1} = 5 a n d a_{2} = 25.

The least positive integer n for which

a_{n} < 0

is
(IIT JEE 2012)

If $a_{1}, a_{2}, a_{3}, \dots \dots$ are in a harmonic progression with $a_{1} = 5$ and $a_{20} = 25$ , then, the least positive integer n for which $a_{n} < 0$ , is

Let $a_{1}, a_{2}, a_{3}, . . . . . . . . . . . . .$ be in harmonic progression with $a_{1} = 5 a n d a_{20} = 25.$ The least positive integer n for which $a_{n} < 0$ is

Join BYJU'S Learning Program

Let a1,a2,a3,............. be in harmonic progression with a1 = 5 and a2 = 25. The least positive integer n for which an < 0 is

Let $a_{1}, a_{2}, a_{3}, . . . . . . . . . . . . .$ be in harmonic progression with $a_{1} = 5 a n d a_{2} = 25.$ The least positive integer n for which $a_{n} < 0$ is