Question

The sum of all odd numbers between $1$ and $1000$ which are divisible by $3$, is

• A. $83667$
• B. $90000$
• C. $83660$
• D. $noneoftheabove$

Answer 1

Answer: (A)

$83667$

Given,

to find the sum of all odd numbers between 1 and 1000 divisible by 3

the series is given by $3,9,15,\mathrm{21...........999}$

$a=3$

$d=9-3=6$

$a_n=999$

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

$999=3+(n-1)6$

$996+6=6n$

$n=167$

$S_n=\frac{n}{2}[a+a_n]$

$=\frac{167}{2}[3+999]$

$=\frac{167}{2}\left[1002\right]$

$=167\left[501\right]$

$=83,667$