If the nth term of the A.P. 9, 7, 5, …. is same as the nth term of

1.	If the nth term of the A.P. 9, 7, 5, …. is same as the nth term of the A.P. 15, 12, 9, … find n.
Answer» 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.

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

Answer»

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.