Question

If the n^th terms of two A.P.s: 9, 7,5 .... and 24, 21, 18, ... are the same, then the value of n is ______.

Answer 1

If the n^th terms of two A.P.s: 9, 7,5 .... and 24, 21, 18, ... are the same, then the value of n is 16.

Explanation:

1^st A.P.: a₁ = 9, d₁ = 7 – 9 = –2

So n^th term t₁ = 9 + (n – 1)(–2) 

= 11 – 2n

2^nd A.P.: a₂ = 24, d₂ = 21 – 24 = –3 

So n^th term t₂ = 24 + (n – 1)(–3) 

= 27 – 3n

Set equal: 11 – 2n = 27 – 3n

⇒ n = 16