Find the sum of all integers less than 1000 that are divisable by 3 but not by 2?

Question

what is the formula? thanks..

Answer 1

Good question.

Numbers divisible by 3 but not by two are odd numbers with increments of 6... ie... 3,9,15,21...

You can get the total number of numbers by dividing

1000/6 = 166.666 - in this case, there would be 167 as 3 and 999 will round you up to 167...

Next, add the highest number 999 with the second lowest number (9) - to get 1008.

9 + 999 = 1008

Now, divide the number of numbers between 9-999 by 2.

166 / 2 = 83

(You divide this because you are summing up two sets of numbers each time... for instance (9+999; 15+993; 21+987, etc) They all add up to 1008. Multiply the two totals:

1008 * 83 = 83664

Then add the original 3 to get your final answer.

83664 + 3 = 83667

Not, you could have added 3 and 999 together multiplied by 83, but then you would have needed to add the midpoint of the 167 numbers you are adding together. Leaving the lowest number out makes things easier in the long run.