Question

Find the sum of all odd integers between $2$ and $100$ divisible by $3$.

• A. $862$
• B. $863$
• C. $865$
• D. $867$

Answer 1

Answer: (D)

The odd integers between $2$ and $100$ which are divisible by $3$ are $3,9,15,21,....99$. Clearly, it is an $A.P$. with first term $a=3$ and common difference $d=6$. Let there be n terms in this sequence. Then,
$a_n=99$
$\Rightarrow 3+(n-1)\times 6=99$
$\Rightarrow n=17$
$\therefore$ Required sum $=\frac{n}{2}\left[a+l\right]$
$=\frac{17}{2}\left[3+99\right]$
$=867$.