Is 68 a term of the A.P. $7, 10, 13, ……$?

Given:

Given A.P. is $7, 10, 13, ……$

To do:

We have to find whether 68 is a term of the given A.P.

Solution:

Here,

$a_1=7, a_2=10, a_3=13$

Common difference $d=a_2-a_1=10-7=3$

If $68$ is a term of the given A.P. then $a_n=68$, where $n$ is a natural number.

We know that,

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

Therefore,

$a_{n}=7+(n-1)(3)$

$68=7+n(3)-1(3)$

$68-7=3n-3$

$61+3=3n$

$3n=64$

$n=\frac{64}{3}$

$\Rightarrow n=21\frac{1}{3}$, which is not a natural number. 

Hence, 68 is not a term of the given A.P.  

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Updated on: 10-Oct-2022

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