SATHEE: Sequences and Series 5 Question 1

Sequences and Series 5 Question 1

1. If $a_{1}, a_{2}, a_{3}, \dots$ 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

(2012)

(a) 22

(b) 23

(d) 25

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Answer:

Correct Answer: 1. (d)

Solution:

PLAN $n$ th term of HP, $t_{n} = \frac{1}{a + (n - 1) n}$

Here, $a_{1} = 5, a_{20} = 25$ for HP

$\begin{aligned} ∴ & \frac{1}{a} & = 5 and \frac{1}{a + 19 d} = 25 \\ \Rightarrow & \frac{1}{5} + 19 d & = \frac{1}{25} \Rightarrow 19 d = \frac{1}{25} - \frac{1}{5} = - \frac{4}{25} \\ ∴ & d & = \frac{- 4}{19 \times 25} \end{aligned}$

Since, $a_{n} < 0$

$\Rightarrow \frac{1}{5} + (n - 1) d < 0$

$\Rightarrow \frac{1}{5} - \frac{4}{19 \times 25} (n - 1) < 0 \Rightarrow (n - 1) > \frac{95}{4}$

$\Rightarrow n > 1 + \frac{95}{4}$ or $n > 24.75$

$∴$ Least positive value of $n = 25$

Sequences and Series 5 Question 1

1. If $a_{1}, a_{2}, a_{3}, \dots$ 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

Answer:

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Sequences and Series 5 Question 1

1. If a1,a2,a3,… are in a harmonic progression with a1=5 and a20=25. Then, the least positive integer n for which an<0, is

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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1. If $a_{1}, a_{2}, a_{3}, \dots$ 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