Question

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

Answer 1

The given AP is 3, 7, 11, 15, ... .

Here, a = 3 and d = 7 − 3 = 4

Let the n^th term of the given AP be 184. Then,

$$\begin{gathered} a_n=184 \\ \Rightarrow 3+\left(n-1\right)\times 4=184\left[a_n=a+\left(n-1\right)d\right] \\ \Rightarrow 4n-1=184 \\ \Rightarrow 4n=185 \end{gathered}$$
$\Rightarrow n=\frac{185}{4}=46\frac{1}{4}$

But, the number of terms cannot be a fraction.

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