# 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

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

$\text { Considering } 9, 7, 5...$

$a = 9, d = \left( 7 - 9 \right) = - 2$

$n^{th} \text { term } = 9 + (n - 1)( - 2) \left[ a_n = a + \left( n - 1 \right)d \right]$

$= 9 - 2n + 2$

$= 11 - 2n . . . (i)$

$\text { Considering } 15, 12, 9, ...$

$a = 15, d = \left( 12 - 15 \right) = - 3$

$n^{th} \text { term } = 15 + (n - 1)( - 3) \left[ a_n = a + \left( n - 1 \right)d \right]$

$= 15 - 3n + 3$

$= 18 - 3n . . . (ii)$

Equating (i) and (ii), we get:

$11 - 2n = 18 - 3n$

$\Rightarrow n = 7$

Thus, 7th terms of both the A.P.s are the same.

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 19 Arithmetic Progression
Exercise 19.2 | Q 14 | Page 12