Arithmetic Sequences Problem 54

Question

What is the sum of all integers between 1 and 6000 which are aren't divisible by 5 or 4?

The only method I could think of is finding all the multiples of 4 and 5 between 1 and 6000 and adding them together. Then finding the sum of all the numbers from 1 to 6000 and subtracting the other sum from this sum to find the answer. But this method isn't at all efficient so can you please help me in finding a method that is efficient?

Do you know how to use a conditional loop in a computer program? I would simple create a list 1 to 6000, go through it and ask the number was divisible by 4 or 5. Then sum this list. Python would be easy. — jfkoehler, Jul 02 '17 at 04:39

score 2 · Accepted Answer · answered Jul 02 '17 at 04:39

2

Sum all the numbers from $1$ to $6000$. The sum of all the multiples of $4$ is four times the sum of all the numbers from $1$ to $1500$. Subtract that. Subtract the sum of all the multiples of $5$. Now the multiples of $20$ .... This is called the inclusion-exclusion principle.

answered Jul 02 '17 at 04:39

Ross Millikan

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would the sum of the numbers that aren't divisible by 5 and 4 between 1 and 6000 be 10800000? – Valerie Jul 02 '17 at 05:43
That is what I get. – Ross Millikan Jul 02 '17 at 14:19

Arithmetic Sequences Problem 54

1 Answers1