--------------------------------------------------------
1 12 15 3
2 12 + 8 = 20 3
3 20 + 8 = 28 6 Pattern starts
4 28 + 5 = 33 6 from Structure 3
5 33 + 8 = 41 9 onwards
6 41 + 5 = 46 9
----------------------------------------------------------
H (119) --> 3 x (119 + 1) / 2 = 180 cm
b) It is 180 cm.
R (119) --> 20 + 8 x (119 - 1)/2 + 5 x (118 - 2)/2 = 782 rods
c) There are 782 rods.
Alternative solution for (c)
-------------------------------
Adjusted Structure 1 --> 20 - 5 = 15
15 , 20 , 28 , 33 , 41 (+ 5 , + 8, + 5, + 8)
R (119) --> 15 + (119 - 1)/2 x (8 + 5) = 782 rods
c) There are 782 rods.
a)correct
ReplyDeleteb)correct
c)not sure
According to what I remember the series were
ReplyDelete1 15
2 20
3 28
4 33
5 41
6 46
Dear PSLE
ReplyDeleteI remember quite clearly that the series was:
1 12
2 20
3 28
4 33
5 41
i guess i am not that experienced or anything, but your formula seems like a lucky guess, because the formula has to be related to the pattern and the number 7 doesn't fit in. forgive me for saying that i think your answer is coincidental.
i think a) and b) are correct (after much "kiasu" discussion with my class. i would identify my class but for fear of shame and embarassment [i know this is so uh...but] i would just say that we are two 6GE classes of 2010) but c) is 782.
method:
first you have to remove number of rods 1 and 2 because they start the pattern and therefore don't fit with the rest of the pattern.
you also have to remove number of rods 3 because 119 is an odd number and you have to add 8 at the end. if you don't remove number of rods 3, you end up adding 8 and 5 alternately, which would not work because you have to add 8 at the end.
from number of rods 4 onwards, 5 and 8 are added respectively alternately.
119-1=118 118/2=59 [119 is the 58 odd number excluding 1 and 3)
5+8=13
58x13=754
remember that you have subtracted number of rods 1, 2 and 3 at first, so you have to add it back.
754+20+8=782
please correct any part of the solution if you find any faults, but i think that this is the right answer.
p.s.and i would be interested in any alternative methods, because mine is very very very very very long...(:
The forumulae are not guess work. You can see the patterns + 8, then + 5.
ReplyDeleteSo to simplify, express the 1st structure in the same pattern.
In examination condition, there is no need to really work out the formulae. Look for the pattern then solve accordingly (as shown in the alternative method for part c).
Hi,
ReplyDeleteI posted the first number in the series wrongly ( regardless of which the answer is 782)- it should be:
1------12
2------20
3------28
4------33
5------41
Thanks for the corrections.
ReplyDeleteChallenging? quite easy
ReplyDelete