# Sequences and series natural numbers

what is the sum of all three digit natural numbers that are multiples of 14, but not 21? What is a quick way of doing sums like these, as i cannot rely on intuition during timed exams

• What do you mean by "cannot rely on intuition"? In a well constructed timed exam you have to rely on intuition to get everything right, because "well constructed" implies that it can distinguish between students who have developed a good intuition for the subject and those who just hammer formulas mindlessly. – hmakholm left over Monica Dec 8 '15 at 11:35
• Ok thats not exactly what i meant, what i meant was i cannot rely on innovation, and the more i have sorted put the better it is – Atharva Dec 8 '15 at 12:58

The three-digit numbers that are divisible by 14 are $$112, 126, \ldots, 994$$ There are $\frac{994-112}{14}+1 = 64$ of them, so their sum is $$64\times\frac{112+994}2$$