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 \ldots \ldots $ find $ n . $

Given:

The two AP series are 9,7,5.... and 15,12,9.....

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

To do:

We have to find the value of n.

Solution:

The first A.P is  9 , 7 , 5 ...

$a_1 = 9  ;  d_1  = 7-9 = - 2$

The second A.P is  15 , 12 , 9...

$a_2 = 15  ;  d_2 = 12-15 = -3$

n^th  term of both the A.P.s are equal.

So, a_n1 $=$ a_n2 

We know that,

a_n = a $+ (n-1)d$

a_n1  $= 9 + (n-1)(-2)$

a_{n 2}  $= 15+(n-1)(-3)$

$9 + (n-1) (-2) = 15 + (n-1) (-3)$

$9 - 2n + 2 = 15 - 3 n + 3$

$11 - 2n =18 - 3n$

$3n - 2n = 18 - 11$

$n = 7$

Therefore,

7^th term of both the A.P s are equal.

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Updated on: 10-Oct-2022

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