Question

In an AP, the mth term 1/n and nth term is 1/m. what is its (mn)th term?  
1. 1/mn
2. n/m
3. 1
4. m/n

Answer 1

Correct Answer - Option 3 : 1

Concept:

Let us consider sequence a₁, a₂, a₃ …. a_n is an A.P.

• Common difference “d”= a₂ – a₁ = a₃ – a₂ = …. = a_n – a_{n – 1}

• n^th term of the A.P. is given by a_n = a + (n – 1) d

 

Calculation:

Let ‘a’ be the first term and ‘d’ be the common difference of an A.P.

Now, given mth term = 1/n

And nth = 1/m

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

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

By subtracting the above two equations, we get, (m-1-n+1) d = 1/n – 1/m

⇒ (m - n)d = (m-n)/mn

⇒ d = 1/mn

Now, (mn)th term = a + (mn -1) d

= a + (mn-1) × 1/mn

= a + 1 – 1/mn  ……(1)

Now,

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

⇒ a = 1/m – (n-1)d

=1/m – (n-1) × 1/mn

= 1/m – 1/m + 1/mn

∴ a = 1/mn

From (1),

(mn)th term = 1/mn + 1  - 1/mn

= 1

Hence, option (3) is correct.