One of the most important question from ML Aggarwal from Arithmetic Progression is to find the sum of all 3 digit natural numbers which are divisible by 7.
Arithmetic Progression chapter 9 question no 21 ii
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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,
an=994
a+(n−1)d=994
105+(n−1)×7=994
n=128
Now, Sn=2n(a+l)
Sn=2128(105+994)=70336.