The season came for ripe apples. On the first day, 1 apple dropped. On the 2nd day...5 apples fell. The next day, 14 apples were lying on the ground, and the 4th day...there were 30 apples.........how many apples would be on the ground on the 10th day and what is the pattern???
everyday after the apples dropped, the little animals would take them, so the numbers aren't the cumulative number of apples falling everyday...
2006-11-28 14:52:34 · 15 answers · asked by jackie N 2 in Science & Mathematics ➔ Mathematics
The animals are just taking the apples that fell the previous day at night, while the next day,,,there are no apples but the ones that fell on that day
2006-11-28 15:54:25 · update #1
forget the animals... that is the distraction
the pattern is that day squared add to the total of the previous day
1 + 2nd day squared (4) = 5
5 + 3rd day squared (9) = 14
14 + 4th day squared (16) = 30
30 + 5th day squared (25) = 55
55 + 6th day squared (36) = 91
91 + 7th day squared (49) = 140
140 + 8th day squared (64) = 204
204 + 9th day squared (81) = 285
285 + 10th day squared (100) = 385
So i guess 385
2006-11-28 15:04:08 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Each day the number of total number apple is equal to the total which are there (fell in previous days) plus the current day squared.
there would be 385 apples on day 10. The pattern is every day, the number of apples which falls is the sum of the squares of all the days. For example, on day 4 the total is 1 squared (1) + 2 squared (4) + 3 squared (9) + 4 squared (16) = 30. This assumes the animals clear all apples every day.
2006-11-28 23:33:15 · answer #2 · answered by Joe J 4 · 0⤊ 0⤋
unless you know how many apples those animals take, no one can tell...
Otherwise, each day, the amount of apples grows by square two (n powered by 2), i.e. 1st day: 1*1 = 1, 2nd day: 5-1 = 4 (2x2); 3rd day: 14-5 = 9 (3x3), etc.
Another words:
1st day = 1x1 (n=1)
2nd day = 1x1 + 2x2 (n=1, 2)
3rd day = 1x1 + 2x2 + 3x3 (n=1, 2, 3)
...
10th day = 1x1 + 2x2 + 3x3 + 4x4 + 5x5 + 6x6 + 7x7 + 8x8 + 9x9 + 10x10 = 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100 = 345
Therefore the overall amount would be a sum of "n powered by 2", where n goes from 1 to 10 (n=1, 2, 3,... 10). The browser doesn't allow me to present it as an equation, but hopefully you get the idea. If there were 30 apples on the 4th day, it was obviously after little animals did the deed. Otherwise, you can always say: 345 minus what the animals have eaten each particular day.
2006-11-28 23:23:13 · answer #3 · answered by Mirta G 2 · 0⤊ 0⤋
Look at the differences between days to find the pattern....
4 apples more between 1st and 2nd day
9 apples more between 2nd and 3rd day
16 apples more between 3rd and 4th day
These are squares of the n-1th day. Continue this through to the 10th day and you get the following number of apples dropping:
1, 5, 14, 30, 55, 91, 140, 204, 285, 385.....385 apples on day 10 (big tree!).
2006-11-28 23:00:04 · answer #4 · answered by sep_n 3 · 0⤊ 0⤋
the differences between the numbers of apples on each day are ascending square numbers
1-0=1
5-1=4
14=5=9
30-14=16
..there's a formula for that but I can't be bothered to work it out. Continuing the series, on the 10th day the number of apples is 385
2006-11-28 22:59:09 · answer #5 · answered by hot.turkey 5 · 0⤊ 0⤋
1
1+2^2
5+3^2
14+4^2
30+5^2
55+6^2
91+7^2
140+8^2
204+9^2
285+10^2
so 10th day the # will be 385
2006-11-28 23:01:54 · answer #6 · answered by raj 7 · 0⤊ 0⤋
It is the squares. Like this 1,2,3,4
1x1=1
2x2=4
you add the 1 and the 4 and you get 5.
third day, 3x3=9
9+5=14
4x4=16
16+14=30
just keep doing the pattern like this.
I believe the answer would be 385 apples.
2006-11-28 23:04:49 · answer #7 · answered by jsfan2510 2 · 0⤊ 0⤋
it's the day number squared, plus the total number of apples that fell the previous day
e.g. (for the third day) -
3 squared = 9
plus 5 (the number of apples that fell on the previous day) = 14.
The fifth day will see 55 apples falling.
plus 30 (number of apples that fell on the previous day) = 55
and so on :P
2006-11-28 22:57:25 · answer #8 · answered by meow3710 2 · 0⤊ 0⤋
woow! that is my favourite question.
you can get the answer from this equation.
T = (n/6)(n + 1)(2n + 1)
you can try it by substitute (n) as the day.
for example, 3rd day, so n is 3
so, while n is 3, the answer is T = (3/6)(3 + 1)((2)(3) + 1) = 14
the apples dropped are 14
so, while n is 10, the answer is T = (10/6)(10 + 1)((2)(10) + 1) = 385
the apples dropped are 385
2006-11-28 23:21:51 · answer #9 · answered by csp 2 · 0⤊ 0⤋
ok...let me answer....
first day it was 1
second day it was 5 = 1 + (2)^2
3rd day it was....14 = 5+(3)^2
4th day it was....30 = 14+(4)^2
hence it is sum(i)=sum(i-1)+(i)^2
continuing the progression we get.....
5th day : 30+5^2 = 55
6th day: 55+6^2 = 91
7th day: 91+7^2 = 140
8th day: 140+8^2 = 204
9th day: 204+9^2 = 285
10th day: 285+10^2 = 385
hence at the end of 10th day....there would be 385 apples
2006-11-28 23:09:20 · answer #10 · answered by Vikram M 2 · 0⤊ 0⤋