Is -150 a term of the AP 11, 8, 5, 2, ....? - Vidyadip

Question

Is -150 a term of the AP 11, 8, 5, 2, ....?

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Answer

The given AP is 11, 8, 5, 2, ...,
Common difference = 8 - 11 = -3
The given term is -150.
The general term of an AP is given by
$a_n = a + (n - 1)d$
$\Rightarrow -150 = a + (n - 1)d$
$\Rightarrow -150 = 11 + (n - 1)(-3)$
$\Rightarrow -150 = 11 - 3n + 3$
$\Rightarrow 3n - 3 = 161$
$\Rightarrow 3n = 164$
$\Rightarrow\text{n}=\frac{164}{3}$
The number of terms cannot be a fraction.
So clearly, -150 is not a term of the AP.

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