Question

Is $51$ a term of the A.P.$5,8,11,14,...?$

Answer 1

$AP=5,8,11,14,...$

Here,$a=5,d=8-5=3$

Let $51$ be the term, say, $nth$ term of this AP.

We know that

$a_n=a+(n-1)d$

So,$51=5+(n-1)\left(1\right)$

$\Rightarrow 51=5+3n-3$

$\Rightarrow 51=2+3n$

$\Rightarrow 51-2=3n$

$\Rightarrow 49=3n$

$\Rightarrow n=\frac{49}{3}$

But $n$ should be a positive integer because $n$ is the number of

terms. So, $51$ is not a term of this given AP.