Question

Is $184$ a term of the sequence $3,7,113$

Answer 1

Find the term of the sequence :

Let the first term be $a$

The common difference $d$

The $n^{th}$ term $a_n=a+\left(n-1\right)d$

Given that,

$a=3$

The second term is $7$

Therefore the common difference is

$$\begin{gathered} d=\mathrm{Second}\mathrm{term}-\mathrm{first}\mathrm{term} \\ \Rightarrow \mathrm{d}=7-3 \\ \Rightarrow \mathrm{d}=4 \end{gathered}$$

Let the $m^{th}$ term be $184$

Therefore

$$\begin{gathered} a_m=a+\left(m-1\right)d \\ \Rightarrow 184=3+\left(m-1\right)4 \\ \Rightarrow 184=3+4m-4 \\ \Rightarrow 184=4m-1 \\ \Rightarrow 185=4m \\ \Rightarrow \frac{185}{4}=m \end{gathered}$$

Clearly $m$ is not a natural number.

Hence, $184$ is not a term of the given sequence.