# 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.

Given: nth term of the A.P. 9, 7, 5,… is same as the nth term of the A.P. 15, 12, 9 …

We know, an = a + (n – 1)d where a is first term or a1 and d is common difference and n is any natural number

Let A.P. 9, 7, 5,… has first term a1 and common difference d1

a1 = 9 and a2 = 7

Common difference, d1 = a2 – a1 = 7 – 9 = -2

Now, an = a1 + (n – 1)d1

an = 9 + (n – 1)(-2)

an = 9 – 2n + 2

an = 11 – 2n

Let A.P. 15, 12, 9 … has first term a1 and common difference d1

b1 = 15 and b2 = 12

Common difference, d2 = b2 – b1 = 12 – 15 = -3

Now, bn = b1 + (n – 1)d2

bn = 15 + (n – 1)(-3)

bn = 15 – 3n + 3

bn = 12 – 3n

According to question:

an = bn

11 – 2n = 12 – 3n

3n – 2n = 12 – 11

n = 1

Hence, the value of n is 1

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 