Find the average of the first 20 counting numbers?

[Guest]

Find the average of the first 20 counting numbers?

[Guest]

All numbers are 20.
The average number is (1 + 20) / 2 = 10.5
20 * 10.5 = 210

[Guest]

Also
1+ 2+ 3+ 4+ ... + 17+ 18+ 19+ 20
20+ 19+ 18+ 17+ ... + 4+ 3+ 2+ 1 Adding vertically
21+ 21+ 21+ 21+ ... + 21+ 21+ 21+ 21

That is a total of 20(21)= 420 but since we have added twice, the sum 1+ 2+ ...+ 19+ 20
is 420/2= 210.

That is, of course, n(n+1)/2 as the previous person said.

[Guest]

And, of course, the "HARD WAY":
20+19= 39. 39+ 18= 57. 57+ 17= 74. 74+ 16= 90. 90+ 15= 105. 105+ 14= 119. 119+ 13= 132. 132+ 12= 144. 144+ 11= 155. 155+ 10= 165. 165+ 9= 174. 174+ 8= 182. 182+ 7= 189. 189+ 6= 195. 195+ 5= 200. 200+ 4= 204. 204+ 3= 207. 207+ 2= 209. 209+ 1= 210. The sum of the first 20 counting numbers is 210 so the average is 210/20= 10.5

[Guest]

Yet another method- 20+ 1= 21, 19+ 2= 21, 18+ 3= 21, down to 11+ 10= 21. There are 10 pairs of numbers that each add to 21 so all 10 pairs add to 10(21)= 210. The average, then, is 210/20= 21/2= 10.5 as before.