Okay, I'm on a quiz bowl team and we have questions like this all of the time. No one on my team knows how to do them. We only have ten seconds to get the answer so we can't go 21+22+23+24...+40. So, I figure there must be some shortcut to figuring this out. Thanks in advance!
2006-10-04 11:45:35 · 10 answers · asked by dr_pepper_dreamr 2 in Science & Mathematics ➔ Mathematics
SHORTCUT IN TERMS THAT CAN BE QUICKLY USED IN A QUIZ
1) Count the number of consecutive numbers you are adding.
2) Half it
3) Add the first and last numbers in the sequence together
3) Multiply the answer from 2) by the answer from 3)
In your case
1) 20
2) 10
3) 61
4) 610
2006-10-04 11:52:30 · answer #1 · answered by Anonymous · 0⤊ 0⤋
549 add the second numbers in the ten numbers first \/
22+23+24+25+26+27+28+29
2+3+4+5+6+7+8+9
5+ 9 + 13 + 17
14 + 30
44+first numbers = 20+20+20+20+20+20+20+20=160
160+44=204 now do it with the 30's good luck with your quiz bowl team :)
2006-10-04 11:53:29 · answer #2 · answered by just tht kid over there 3 · 0⤊ 1⤋
1+2+3+...+N = N(N+1)/2
1+2+3+...20 = 21*20/2 = 210 = s1
1+2+3+...+40 = 41*40/2 = 820=s2
21+22+23+...+40 = s2-s1 = 610
2006-10-04 11:54:12 · answer #3 · answered by Anonymous · 0⤊ 0⤋
there is a shortcut to figure it out
suppose you want the sum of all numbers from 3 to 8
write down the numbers
3 4 5 6 7 8
now write them in reverse
8 7 6 5 4 3
add them
11 11 11 11 11 11
add the 11s = 66
divide by 2 is 33
33 is the answer
2006-10-04 11:49:36 · answer #4 · answered by Anonymous · 0⤊ 1⤋
This is an arithmetic progression with first term a1= 21, last term equal an=40 and difference d=1.
Find the number of terms n from the formula:
An = A1 + (n-1) * d
The sum is
Sn = n [2*A1 + (n-1) * d] /2
2006-10-04 11:57:25 · answer #5 · answered by Dr. J. 6 · 0⤊ 1⤋
21+29=50
22+28=50
23+27=50
24+26=50
31+39=(21+10)+(29+10)=50+20
32+38=50+20
33+37=50+20
34+36=50+20
200+200+80+25+35=
480+60=540 use addition's properties to your advantage. remember your algerbra?!
2006-10-04 12:01:21 · answer #6 · answered by matt2571483 2 · 0⤊ 1⤋
(21+40)*20/2=610, it is an arithmetic progression
2006-10-04 11:50:13 · answer #7 · answered by jaime r 4 · 0⤊ 0⤋
(21+40)*10=610
2006-10-04 11:51:32 · answer #8 · answered by John P 1 · 0⤊ 0⤋
88
2006-10-04 11:46:50 · answer #9 · answered by Anonymous · 0⤊ 1⤋
(min value + max value) * quantity of numbers to add / 2
in using your example you would have
(21+40) * 20/2
2006-10-04 12:00:40 · answer #10 · answered by jamg78 4 · 0⤊ 0⤋