Is 302 a term of the A.P. $3, 8, 13, …..$?

Given:

Given A.P. is $3, 8, 13, …..$

To do:

We have to find whether 302 is a term of the given A.P.

Solution:

Here,

$a_1=3, a_2=8, a_3=13$

Common difference $d=a_2-a_1=8-3=5$

If $302$ is a term of the given A.P. then $a_n=302$, where $n$ is a natural number.

We know that,

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

Therefore,

$a_{n}=3+(n-1)(5)$

$302=3+n(5)-1(5)$

$302-3=5n-5$

$299+5=5n$

$5n=304$

$n=\frac{304}{5}$

$\Rightarrow n=60\frac{4}{5}$, which is not a natural number. 

Hence, 304 is not a term of the given A.P.   

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Updated on: 10-Oct-2022

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