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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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