+0

# help

0
59
2

Find the sum of the multiples of 19 or 5 under 775

Guest May 25, 2017

#2
+75344
+1

The number of multiples of 19 < 775  =  775 / 19  =  40

And their sum  =   19 (40)(41)/2  = 15580

The number of multiples of 5 < 775  =  770 / 5 =   154

And their sum  =  5 (154)(155) / 2  =  59675

However....we must subtract out the sum of all numbers divisible by both 5 and 19.......this will equal all the multiples  of 19 * 5  = 95.......so  775/95  =  8

So...the sum of these  = 95 (8) (9)/2  =  3420

So...the total sum of all multiples of 5 or 16 less than 775  =  [ 15580 + 59675 - 3420 ]  = 71835

CPhill  May 25, 2017
Sort:

#1
0

Find the sum of the multiples of 19 or 5 under 775.

Well, the easiest way to do it is as follows:

775 / 19 =40.7894....... Just drop the fraction and keep 40. That means there are 40 multiples of 19 up to 775.

Now, you can use an Arithmetic Progression to add them up:

Sum =n/2[2a + (n - 1)d] =40/2[2*19 + (40 - 1)*19] =20[38 + 741] =15,580 - which is the total of all multiples of 19 up to 775.

Now, do exactly the same thing with 5 =775 / 5 =155. This is how many multiples of 5 you have up to 775.

Use the same formula as above to add them all up. If you do it right, you should get a total of =60,450. Now, try to see if you get the same number. Good luck.

Guest May 25, 2017
edited by Guest  May 25, 2017
#2
+75344
+1

The number of multiples of 19 < 775  =  775 / 19  =  40

And their sum  =   19 (40)(41)/2  = 15580

The number of multiples of 5 < 775  =  770 / 5 =   154

And their sum  =  5 (154)(155) / 2  =  59675

However....we must subtract out the sum of all numbers divisible by both 5 and 19.......this will equal all the multiples  of 19 * 5  = 95.......so  775/95  =  8

So...the sum of these  = 95 (8) (9)/2  =  3420

So...the total sum of all multiples of 5 or 16 less than 775  =  [ 15580 + 59675 - 3420 ]  = 71835

CPhill  May 25, 2017

### 8 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details