Which term of the A.P. $4, 9, 14, …..$ is $254$?

Given:

Given A.P. is $4, 9, 14, …..$

To do:

We have to find $254$ is which term of the given A.P.

Solution:

Let $254$ be the nth term of the given A.P.

Here,

$a_1=4, a_2=9, a_3=14$

Common difference $d=a_2-a_1=9-4=5$

We know that,

nth term $a_n=a+(n-1)d$

Therefore,

$a_{n}=4+(n-1)(5)$

$254=4+n(5)-1(5)$

$254-4=5n-5$

$250+5=5n$

$5n=255$

$n=\frac{255}{5}$

$n=51$

Hence, $254$ is the 51st term of the given A.P.   

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Updated on: 10-Oct-2022

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