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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Updated on: 10-Oct-2022

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