# 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. - Mathematics

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.

#### Solution

Here, we are given two A.P. sequences whose nth terms are equal. We need to find n.

So let us first find the nth term for both the A.P.

First A.P. is 9, 7, 5 …

Here

First term (a) = 9

Common difference of the A.P. (d) = 7 - 9

= -2

Now as we know

a_n = a + (n - 1)d

So for nth term

a_n = a + (n -1)d

So for nth term

a_n = 9 + (n -1)(-2)

= 9 - 2n + 2

= 11 - 2n  .......(1)

Second A.P. is 15, 12, 9 …

Here,

First term (a) = 15

Common difference of the A.P. (d) = 12 - 15

= -3

Now as we know

a_n = a + (n - 1)d

So for nth term

a_n = 15 + (n -1)(-3)

= 15 - 3n + 3

= 18 - 3n .....(2)

Now, we are given that the nth terms for both the A.P. sequences are equal, we equate (1) and (2),

11 - 2n = 18 - 3n

3n - 2n = 18 - 11

n = 7

Therefore n = 7

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 5 Arithmetic Progression
Exercise 5.4 | Q 12 | Page 25