Check, whether $-150$ is a term of the AP: $11, 8, 5, 2, ….$

Given:

Given A.P. is $11, 8, 5, 2, …..$

To do:

We have to check whether $-150$ is a term of the given A.P.

Solution:

Here,

$a_1=11, a_2=8, a_3=5, a_4=2$

Common difference $d=a_2-a_1=8-11=-3$

If $-150$ is a term of the given A.P. then $a_n=-150$, where $n$ is a natural number.

We know that,

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

Therefore,

$a_{n}=11+(n-1)(-3)$

$-150=11+n(-3)-1(-3)$

$-150-11=-3n+3$

$161+3=3n$

$3n=164$

$n=\frac{164}{3}$

$\Rightarrow n=54\frac{2}{3}$, which is not a natural number. 

Hence, $-150$ is not a term of the given A.P.     

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Updated on: 10-Oct-2022

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