Question

Is $184$ a term of the sequence $3,7,11,...$?

Answer 1

Clearly, the given sequence is an A.P. with first term $a(=3)$ and common difference $d(=4)$.

Let the $n^{th}$ term of the given sequence be $184$. Then,
$a_n=184$

$⟹a+(n-1)d=184$
$⟹3+(n-1)\times 4=184⟹4r=185⟹n=46\frac{1}{4}$
Since $n$ is not a natural number. So, $184$ is not a term of the given sequence.