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The sum of all the multiples of 3 or 5 below 1000?
The multiple of 3 nearest to and below 1000 is 999. 999/3 = 333 The sum of all the multiples is 3 x 333 x 334/2 = 166833 The multiple of 5 nearest to and below 1000 is 995. 995/5 = 199 The sum of all the multiples is 5 x 199 x 200/2 = 99500
What is the sum of the multiples of 9?
There are infinitely many multiples of 9 and it is not possible to add them all.
What is the sum of all integers not greater than 10000 that are not divisible by 7?
This is easiest to answer by summing all the numbers 1-10000 and subtracting the sum of the multiples of 7 (7, 14, 21, ..., 9996). The sum of a series is: S = (first + last) x number_of_terms / 2 For for 1-10000, the sum is: S1 = (1 + 10000) x 10000 / 2 = 10001 x 5000 = 50005000 For the multiples of 7 the sum is: S2 = (7 + 9996) x 1428 / 2 = 10003 x 714 = 7142142 So the sum of all integers not greater than 10000 that are not divisible by 7 is: S = S1 - S2 = 50005000 - 7142142 = 42,862,858
What is the sum of all the odd numbers below 100?
The sum is 10,000
One half of the sum of three consecutive multiples of 10 is 90 What are the multiples of 10?
If half of the sum is 90 then the full sum must be 180. The three consecutive multiples of 10 which add up to 180 are 50, 60 and 70.
