Find $n$ if the given value of $x$ is the nth term of the given A.P.
$ 25,50,75,100, \ldots ; x=1000 $

Given:

Given A.P. is \( 25,50,75,100, \ldots \)

$x=1000$ is the nth term of the A.P.
To do:
 We have to find the value of $n$.

Solution:

We know that,

nth term of an A.P. $a, a+d, a+2d,.....$ is $a_n=a+(n-1)d$.

In the given A.P.,

$a_1=25, a_2=50, a_3=75$ and common difference $d=50-25=25$

This implies,

$x=25+(n-1)25$

$1000=25+25n-25$

$25n=1000$

$n=\frac{1000}{25}$

$n=40$

The value of $n$ is $40$.

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Updated on: 10-Oct-2022

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