Question

If the n^th term of the A.P. 9, 7, 5, …. is same as the n^th term of the A.P. 15, 12, 9, … find n.

Answer 1

Given,

A.P₁ = 9, 7, 5, …. and A.P₂ = 15, 12, 9, …

And, we know that, n^th term a_n = a + (n – 1)d

For A.P₁,

a = 9, d = Second term – first term = 9 – 7 = -2

And, its n^th term a_n = 9 + (n – 1)(-2) = 9 – 2n + 2

a_n = 11 – 2n …..(i)

Similarly, for A.P₂

a = 15, d = Second term – first term = 12 – 15 = -3

And, its n^th term a_n = 15 + (n – 1)(-3) = 15 – 3n + 3

a_n = 18 – 3n …..(ii)

According to the question, its given that

n^th term of the A.P₁ = n^th term of the A.P₂

⇒ 11 – 2n = 18 – 3n

n = 7

Therefore, the 7^th term of the both the A.Ps are equal.