Find $n$ if the given value of $x$ is the nth term of the given A.P.
$ 5 \frac{1}{2}, 11,16 \frac{1}{2}, 22, \ldots ; x=550 $

Given:

Given A.P. is \( 5 \frac{1}{2}, 11,16 \frac{1}{2}, 22, \ldots \)

$x=550$ 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.,

$a_1=5\frac{1}{2}, a_2=11, a_3=16\frac{1}{2}$ and common difference $d=11-5\frac{1}{2}=11-\frac{5\times2+1}{2}=\frac{11\times2-11}{2}=\frac{11}{2}$

This implies,

$x=5\frac{1}{2}+(n-1)(\frac{11}{2})$

$550=\frac{11}{2}+\frac{11}{2}n-\frac{11}{2}$

$550=\frac{11}{2}n$

$n=\frac{2}{11}\times550$

$n=2\times50$

$n=100$

The value of $n$ is $100$. 

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Updated on: 10-Oct-2022

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