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

Question:

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

 

Solution:

The given AP is 11, 8, 5, 2, ... .

Here, a = 11 and d = 8 − 11 = −3

Let the nth term of the given AP be −150. Then,

$a_{n}=-150$

$\Rightarrow 11+(n-1) \times(-3)=-150 \quad\left[a_{n}=a+(n-1) d\right]$

$\Rightarrow-3 n+14=-150$

$\Rightarrow-3 n=-164$

$\Rightarrow n=\frac{164}{3}=54 \frac{2}{3}$

But, the number of terms cannot be a fraction.

Hence, −150 is not a term of the given AP.

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