Find $n$ if the given value of $x$ is the nth term of the given A.P.
$ -1,-3,-5,-7, \ldots ; x=-151 $

Given:

Given A.P. is \( -1,-3,-5,-7, \ldots \)

$x=-151$ 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.,

$a_1=-1, a_2=-3, a_3=-5$ and common difference $d=-3-(-1)=-3+1=-2$

This implies,

$x=-1+(n-1)(-2)$

$-151=-1-2n+2$

$2n=1+151$

$2n=152$

$n=\frac{152}{2}$

$n=76$

The value of $n$ is $76$.

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Updated on: 10-Oct-2022

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