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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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