NIMCET 2018 Question Paper with solutions

Question : 43 of 120

Marks: +1, -0

Suppose that m and n are fixed numbers such that the mth term

a_m

is equal to n and the nth term

a_n

is equal to m (m ≠ n) , then the

(m+n)^{\th}

term is

Solution:

Given that, m th term of H.P

1/n = 1/a + (m - 1) d ... (i)

and n th term

1/m = 1/a + (n - 1) d ... (ii)

Subtract Eq. (ii) from Eq. (i), we get

1/n-1/m = 1/a + (m - 1) d - 1/a - (n - 1) d

⇒ {m-n}/{mn} = d [m - 1 - n + 1]

⇒ d = 1/{mn}

Put the value of d in Eq. (i)

1/n = 1/a+{m-1}/{mn}

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

a= mn

∴ T_{m+n} = 1/{1/{mn}+(m+n-1)1/{mn}}

= 1/{{1+m+n-1}/{mn}} = {mn}/{m+n}

Go to Question:

Prev Question

Next Question