Find: Is -150 a term of the A.P. 11,8,5,2, . . ? - Vidyadip

Question

Find:
Is $-150$ a term of the A.P. $11,8,5,2, \ldots . . ?$

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Answer

In the given problem, we are given an A.P. and the Value of one of its term.
We need to find whether it is a term of the A.P. or not so here we will use the formula $a_n=a+(n-1) d$.
Here,
A.P. is $11,8,5,2, \ldots .$.
$a_n=-150, a=11$ and $d=8-11=-3$
Thus, using the above mentioned formula, we get
$-150=11+(n-1)(-3)$
$\Rightarrow-150-11=-3 n+3$
$\Rightarrow-161=-3 n+3$
$\Rightarrow-161-3=-3 n$
$\Rightarrow-3 n=-164$
$\Rightarrow n=\frac{164}{3}$
Since, the value of n is a fraction. Thus, $-150$ is not the term of the given A.P.

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