Question

What is the number of terms in the series $117,120,123,126,..,333$ ?

• A. $72$
• B. $73$
• C. $76$
• D. $79$

Answer 1

The correct option is B $73$

$117,120,123,126,....,333$

As we can see the difference of $1^{st}$ and $2^{nd}$ and that of $2^{nd}$ and $3^{rd}$ and so on is $120-117=3$.

So the common difference $=3$

Let $333$ is the $n^{th}$ term

So, $a+(n-1)d=333$

where $a=117$ and $d=3$

$\Rightarrow 117+(n-1)3=333\Rightarrow (n-1)3=216\Rightarrow n-1=\frac{216}{3}\Rightarrow n=72+1\Rightarrow n=73$

Answer $\left(B\right)$