Is 184 a term of the AP 3, 7, 11, 15, …?
Question:

Is 184 a term of the AP 3, 7, 11, 15, …?

Solution:

The given AP is 3, 7, 11, 15, … .

Here, a = 3 and d = 7 − 3 = 4

Let the nth term of the given AP be 184. Then,

$a_{n}=184$

$\Rightarrow 3+(n-1) \times 4=184 \quad\left[a_{n}=a+(n-1) d\right]$

$\Rightarrow 4 n-1=184$

$\Rightarrow 4 n=185$

$\Rightarrow n=\frac{185}{4}=46 \frac{1}{4}$

But, the number of terms cannot be a fraction.

Hence, 184 is not a term of the given AP.

 

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