## wintersuntime one year ago Can someone be nice enough to help me please with this worksheet -> http://crsearch.fcps.edu/crsearch/retrieveresourcefile.cfm?hxresid=R001EED

1. wintersuntime

It's the one of building staircases

2. dan815

what are you confused about?

3. wintersuntime

about how to get 100

4. dan815

what do you mean

5. dan815

6. wintersuntime

what is the total numbers of cubes how many steps I need in 100

7. dan815

ah okay like this

8. dan815

|dw:1438307419721:dw|

9. dan815

|dw:1438307470634:dw|

10. dan815

you see how the number of cubes needed is increasing for each step

11. wintersuntime

yes but I need to find out the total number of cubes

12. wintersuntime

for 100

13. dan815

right look at this pattern

14. dan815

for 1 step its 1 for 2 its 1+2 for 3 its 1+2+3 for 100 its 1+2+3+4....+99+100

15. dan815

you have to see what the sums upto

16. dan815

there is a trick to find out what that sums upto

17. dan815

|dw:1438307608134:dw|

18. dan815

if you add the first and last together the 2nd and 2nd last the 3rd and 3rd last they all give u the same number

19. dan815

how many of those additions will there be if u add this way

20. dan815

there is another way to look at it

21. dan815

lets take a simpler example

22. dan815

1+2+3+4+5 = ?

23. dan815

what you can do is rewrite another replica of it backwards 1+2+3+4+5=? 5+4+3+2+1=? --------------- 6+6+6+6+6= 5*6 --------------- we added 2 sums we only want to find out 1+2+3+4+5 so we divide 5*6 by 2= 5*6/2= 30/2=15 so 1+2+3+4+5=15

24. dan815

we can use this same trick for this 1+2+3+4+5+6.....99+100

25. dan815

can you figure that out

26. dan815
27. wintersuntime

so for 100 its 99

28. wintersuntime

@dan815

29. dan815

so for 1 to 100

30. dan815

lets do a smaller example how about 1 to 10

31. dan815

1+2+3+4+5+6+7+8+9+10=? remember the trick from before?

32. dan815

lets add this set back to itself

33. dan815

1+2+3+4+5+6+7+8+9+10=? 10+9+8+7+6+5+4+3+2+1 =? now add each column ------------------------------ 11+11+11+11...+11 =? how many 11s will there be?