JIPMAT 2021 (QA) - If the m^th term of an arithmetic progression is 1/n and the n^th term is 1/m, then the mn^th term of this progression will be | PYQs + Solutions

JIPMAT 2021

Algebra

Progression & Series

Conceptual

If the $m^{\text{th}}$ term of an arithmetic progression is $\frac{1}{n}$ and the $n^{\text{th}}$ term is $\frac{1}{m}$ , then the $mn^{\text{th}}$ term of this progression will be

\frac{1}{mn}

\frac{m}{n}

\frac{n}{m}

Correct Option: 4

Given:

\newline

a_m = \frac{1}{n}

and

a_n = \frac{1}{m}

From arithmetic progression formula:

\newline

a + (m-1)d = \frac{1}{n}

...(1)

a + (n-1)d = \frac{1}{m}

...(2)

Subtracting (2) from (1):

\newline

(m-n)d = \frac{1}{n} - \frac{1}{m}

(m-n)d = \frac{m-n}{mn}

d = \frac{1}{mn}

Substituting back in (1):

\newline

a + (m-1)\frac{1}{mn} = \frac{1}{n}

a = \frac{1}{n} - \frac{m-1}{mn}

For

mn^{th}

term:

\newline

a_{mn} = a + (mn-1)d

= [\frac{1}{n} - \frac{m-1}{mn}] + (mn-1)\frac{1}{mn}

= \frac{mn}{mn} = 1

Therefore, the

mn^{th}

term is 1.