Question

Find the sum of all three-digit natural numbers which are divisible by 7.

Answer 1

All three-digit natural numbers which are divisible by 7 are

$105,112,119,126,...,994$ which are in AP with $a=105,d=7,l=994$

Let the number of these terms be n. Then,

$a_n=994$

$a+(n-1)d=994$

$105+(n-1)\times 7=994$

$n=128$

Now, $S_n=\frac{n}{2}(a+l)$

$S_n=\frac{128}{2}(105+994)=70336$.