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Find whether 0 (zero) is a term of the A.P. $40, 37, 34, 31, ……$
Given:
Given A.P. is $40, 37, 34, 31, ……$
To do:
We have to find whether $0$ is a term of the given A.P.
Solution:
Here,
$a_1=40, a_2=37, a_3=34$
Common difference $d=a_2-a_1=37-40=-3$
If $0$ is a term of the given A.P. then $a_n=0$, where $n$ is a natural number.
We know that,
nth term $a_n=a+(n-1)d$
Therefore,
$a_{n}=40+(n-1)(-3)$
$0=40+n(-3)-1(-3)$
$0-40=-3n+3$
$3n=40+3$
$3n=43$
$n=\frac{43}{3}$
$\Rightarrow n=14\frac{1}{3}$, which is not a natural number.
Hence, 0 is not a term of the given A.P.   
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