Find the sum of all three digit natural numbers which are multiples of 7.

The three digit numbers which are multiples of7are105,112,119,...,994a2−a1=112−105=7a3−a2=119−112=7∵a3−a2=a2−a1=7Therefore, the series is in APHere,a=105,d=7andan=994We know that,an=a+(n−1)d⇒994=105+(n−1)7⇒994−105=(n−1)7⇒889=(n−1)7⇒127=(n−1)⇒n=128Now, we have to find the sum of this APSn=n2[2a+(n−1)d]⇒S128=1282[2×105+(128−1)7]⇒S128=64[210+127×7]⇒S128=64[1099]⇒S128=70336Hence, the sum of all three digit numbers which aremultiple of7are70336.