Question

Find the sum of odd integers between $1$ and $1000$ which are divisible by $3$.

• A. $83667$
• B. $54954$
• C. $99994$
• D. $79894$

Answer 1

Answer: (A)

$83667$

Odd integers divisible by 3 are: $3,9,15,\mathrm{21.....999}$

Let $a=3$ and $d=6$

$\therefore T_n=999=3+(n-1)6$

$\Rightarrow n-1=\frac{996}{6}=166$

$\therefore n=167$

$\therefore S_n=\frac{167}{2}[2\times 3+(167-1\left)6\right]=83667$