How many multiples of 5 are between 100 and 1000?

Answer 1

15*7 = 105

142*7 = 994

So the question is equivalent to finding the sum: 105 + 112 + 119 + ... + 994

= 7*(15 + 16 + 17 + ... + 142)

= 7*(142*143/2 - 14*15/2)

= 7*(10153 - 105)

= 7*10048

= 70336

Answer 2

This is the sum S = 105 + 110 + ... + 995

This is a sequence whose nth term is a+r*n where a = 100, r (the common difference) = 5 and n = 1,2,3, ... , 179, so that N = max(n) = 179.

Then S = N *[a + (N+1)*r/2] = 179*[100+180*5/2] = 179*(100+450) = 179*550 = 98450.

Another way to solve this is to work in one-fifths and then multiply the answer by 5 at the end. So,

(1) add all the whole numbers from 1 to 199 (similar to multiples of 5 from 5 to 995);

(2) subtract from this the sum of all whole numbers from 1 to 20 (multiples in subtract 5 to 100) so you are left with the sum of all whole numbers from 21 to 199 (105 to 995);

(3) multiply this answer by 5.

Answer 3

1000, 1010, 1020, 1030, 1040, 1050, 1060, 1070, 1080, 1090 and 1100.

Answer 4

19: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95.

Answer 5

179 of them.

Answer 6

There are 179.

Answer 7

60.

Answer 8

13 of them.