Question

The sum of all natural numbers less than $400$ which are not divisible by $6$ is

• A. $13266$
• B. $66534$
• C. $79800$
• D. $93066$

Answer 1

The correct option is B $66534$

Sum of all natural number less than $400$ $=\frac{1}{2}\times 399\times 400=79800$
Now the number which are divisible by $6$ are in A.P
$6,12,18,24,\mathrm{30...396}$
So here $a=6,d=6,a_n=396$
To find the number of terms
$a_n=a+(n-1)d$
$396=6+(n-1)\times 6$
$396=6+6n-6$
$n=66$
Sum of natural number which are divisible by $6$.
$s_n=\frac{66}{2}\times (6+396)$
$s_n=66\times 201=13266$
By subtracting sum of natural number from sum of natural number divisible by $6$ will get the sum of natural number which not divisible by $6$.
Sum of natural number which not divisible by $6$ $=79800-13266=66534$.