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Your task to do....
You may have seen this sequence before:
1,1,2,3,5,8,13,21,...
It is called the Fibonacci Sequence, and each term is calculated by adding together the previous two terms in the sequence.
- Try adding together any three consecutive Fibonacci numbers.
- Choose any four consecutive Fibonacci numbers. Add the first and last, and divide by two.
- Add together any six consecutive Fibonacci numbers and divide by four.
- Can you discover any Fibonacci Surprises of your own?
This comment has been removed by the author.
ReplyDeleteThis comment has been removed by the author.
Delete1) all of the sums of three numbers are even.
ReplyDelete2) it's in a pattern, the first answer is even then the next two is odd and so on so forth.
3) each answer turns out to be a number part of the Fibonacci sequence.
4) Remarkably, you can use consecutive terms to convert miles to kilometers:
8 miles ≈ 13 kilometers
13 miles ≈ 21 kilometers
1. 1+1+2=4 I noticed that the previous term's value is added to the next term.
ReplyDelete2. 1+3=4/2=2 I notice that the answer is same as the third term.
3. 1+1+2+3+5+8=20/4=5 I notice that the answer is same as the fifth term.
4. No
w/ fudail farhan
1)1+2+3=6
ReplyDeleteI notice that the first two numbers I added;the answer is equal to the other number
2)1+5/2=3
5+21/2=13
I noticed that the units in the answer is 3 for both of them
3)1+2+3+5+8+13+21/4=8
2+3+5+8+13+21/4=13
I noticed that there is no connection between them
First: 1+2+3= 6.
ReplyDelete2+3+5= 10.
i noticed that the first two numbers you added ,its answer is equal to the number you are adding.
Second: 1+5/2-3
I noticed that the units in the answers is 3
Third: 1+2+3+5+8+13/4=8
2+3+5+8+13+21/4=13
I noticed that there was no connection between them.
. 1+1+2=4 I noticed that the previous term's value is added to the next term.
ReplyDelete. 1+3=4/2=2 I notice that the answer is same as the third term.
. 1+1+2+3+5+8=20/4=5 I notice that the answer is same as the fifth term.
. No
1A: I can notice that the number's product is double than the last number in the set. ie. 1+1+2=4, 2*2=4
ReplyDelete2A: I can notice that the number's product is double than the second last number in the set. ie.1,1,2,3, 1+3=4, 2*2=4
3A: I can notice that the number's product is the second last number multiplied by four. ie. 1,1,2,3,5,8 1+1+2+3+5+8=20, 20/4=5
4A: Yes, 1 is the only number that is repeated.
w/ John
Delete1.1+1+2=3
ReplyDeletethe previous terms add together
2.1+3=4/2=2
minus the first 2 terms
3.1+1+2+3+5+8=20/4=5
the answer is the same as the 5th term
4.the sequence goes in this pattern:odd,odd,even,odd,odd,even and so on.
1+1+2=4
ReplyDelete1+2+3=6
3+5+8=16
I fylu add three consecutive fibonacci numbers,the answer is always even,and the answer is also the double of the last number of the values.
2.
1,1,2,3 1+3=4 4/2=2
5,8,13,21 5+21=26 26/2=13
The final answer is always the number after the last value of the 4 consecutive fibonacci numbers.
3. 1+1+2+3+5+8=20. 20/4=5
2+3+5+8+13+21=52. 52/4=13
Just like the second question the answer is also the equal to second to the last value of the consective fibonacci numbers.
1) 2+3+5=10
ReplyDeleteI realized that when i add the first two numbers, it adds up to the third number.
2) 1+5 divided by 2 = 3; 3 was the third number out of the four consecutive numbers i have chosen.
3)1+1+2+3+5+8=20 divided by 4 =5
I realized that the answer is similar to the fifth term of the six consecutive numbers i have chosen.
4) They go in a sequence that is: odd, odd, even .....
Math blog
ReplyDeleteQ1Ans. I have notified that we can add a fibonacc number is a rule of series of numbers in a triangle. And when we add any three consecutive fibonacci numbers for example (1+1+2= 4) and that can be a consecutive numbers.
Q2Ans. I have noticed and understand that we add a fibonacci number by adding for example (1,1,2,3) and I have added the first number its: (1) and the last its: (3) and i have added both of them and i have got (4) as the answer and i divided the: (4) by the: (2) and i have gotten the ans: (2).
Q3Ans. I have notified that when I have added the first 6 numbers that: (1,1,2,3,5,8) and when u have added all of them i have gotten the answer is: (20) and when I have divided 20/4 I have gotten the answer: (5).
Q1)I have noticed that when ever you add the two previous numbers you will get the next number, for example as shown above eg:1+1=2 then 2+1=3 then 3+2=5 just like 1,1,2,3,5 the previous two just gets added to get the next number.
ReplyDeleteQ2)I will choose 1,1,2,3 and when i add the first and the last number i will of course get the answer 4 and now i need to divide this number by 2, the answer will be 2 since 3+1=4 then 4/2=2. I noticed that the number's product is double than the second last number in the set. ie.1,1,2,3, 1+3=4, 2*2=4
Q3)I can notice that the number's product is the second last number multiplied by four. ie. 1,1,2,3,5,8 1+1+2+3+5+8=20, 20/4=5
2 + 3 + 5 = 10
ReplyDeleteYou get even numbers. When we add three consecutive Fibonacci numbers, the results will be even.
2, 3, 5, 8
8 + 2 = 10 ÷ 2 = 5
The answer is the numbers from the Fibonacci Sequence.
1 + 1 + 2 + 3 + 5 + 8 = 20
20 ÷ 4 = 5
The answers are also from the Fibonacci Sequence.
No.
ans 1: 3+5+8=16 16 is not part of fibonacci series.
ReplyDeleteans 2: add 0.5 then 1.0 then 1.5 then 2.0...etc. starting from the 1st 4 numbers
ans 3: when you add the 6 terms and divide by 4 you get the 2nd highest term.
ans 4:
By: Ayman abdul Ghaffar 8D
A) 1+1+2=_4_
ReplyDelete1+2+3=_6_
2+3+5=_10_
The answers are even numbers.
B) 13,21,34,55
55+13=68
68/2=_34_
The answer is part of the sequence.
C) 8,13,21,34,55,89
Total=220
220/4=_55_
The answer is part of the sequence and is an odd number.
D) E,O,O,E,O,O,E,O,O...
E=Even number
O=Odd number
By:Nathaniel 8D
5, 8, 13
ReplyDeleteSo 5+8+13= 26
To what I have noticed, when I added the three consecutive numbers; the outcome is an even number as shown above.. It also happens with the rest of the other consecutive fibonacci sequence like- 2+3+5 gives you 10. Or 1+1+2=4. For the second question, I have chosen 2, 3, 5, 8. So, 2+8=10÷2=5 (fibonacci number) Also, 1, 1, 2, 3. So, 1+3=4÷2=2(fibonacci sequence). You can observe that the results are from the fibonacci sequence. Now for the third, I chose 2, 3, 5, 8, 13, 21 which gives 52 and divided it by 4; the result is 13 which again is answer from the sequence.. For what I know, these fibonacci sequence have codes behind them although not sure of it.. That's the smallest discovery I have made.
Ans1 if you add any 3 fibonacci consecertive numbers the product is notgoing to appeare in,the sequence
ReplyDeleteAns2 when you add the fuor consectecative numbers and divide by 2 it will be the 3rd
Number
Ans3 if you add the 6 terms and divide 4 you get the 5 term
Ans4 the sequence is odd odd even odd odd even
JAnswer1)1+1+2=4. 8+13+21=42
ReplyDeleteIf we add any 3 Fibonacci numbers we get an even number.
Answer2) 1,1,2,3
3+1=4. 4\2=4
3,5,8,13
3+13=16. 16\2=8
If we take any 4 consecutive Fibonacci numbers and add the first and the last and divide it by 2. we will get a number which is in the Fibonacci sequence.
Answer3)1+1+2+3+5+8=20. 20\4=5
2+3+5+8+13+21=52. 52\4=13
If we add any 6 consecutive fibonacci numbers the answer which we get is the 2nd last number of the 6 chosen number.
By Waleed Shaikh and Shahmir
DeleteBy Waleed Shaikh, Mubariz and Shahmir
Delete1) 3+5+8=16 16 is not part of fibonacci series.
ReplyDelete2) add 0.5 then 1.0 then 1.5 then 2.0...etc. starting from the 1st 4 numbers
3)when you add the 6 terms and divide by 4 you get the 2nd highest term.
1) 3+5+8=16 16 is not part of fibonacci series.
ReplyDelete2) add 0.5 then 1.0 then 1.5 then 2.0...etc. starting from the 1st 4 numbers
3)when you add the 6 terms and divide by 4 you get the 2nd highest term.
This comment has been removed by the author.
ReplyDeleteBy Waleed Shaikh and Shahmir
ReplyDelete
ReplyDelete1. Fibonacci sequence’s pattern is odd, odd, even. Adding 3 consecutive numbers in the Fibonacci sequence it gives all of the answer as an even number
2. The answer is the number in the Fibonacci sequence. The sequence starts at 2 and it continues
3. The sequence is the third number in the Fibonacci sequence.
4. Fibonacci numbers have a property that the ratio of two consecutive numbers tends to the Golden ratio as numbers get bigger and bigger. The Golden ratio is a number and it happens to be approximately 1.618.
Coincidentally, there are 1.609 kilometers in a mile, which is within 0.5% of the Golden ratio.
If we take two consecutive Fibonacci numbers, Fn+1 and Fn, we know that their ratio Fn+1/Fn is approximately 1.618. Since the ratio is also almost the same as kilometers per mile, we can write Fn+1/Fn = [mile]/[km]. It follows that Fn•[mile] = Fn+1•[km], which translates to English as "n-th Fibonacci number in miles is the same as (n+1)-th Fibonacci number in kilometers".
That's all there is to it. A pure coincidence that the Golden ratio is almost the same as kilometers in a mile.
You may have seen this sequence before:
ReplyDelete1,1,2,3,5,8,13,21...
It is called the Fibonacci sequence, and each term is calculated by adding together the previous two terms in the sequence.
Try adding together any three consecutive Fibonacci numbers.
What do you notice? Can you explain it?
1+1+2=4 =2*2
3+5+8=16 = 8*2
13+21=34*2 = 68
Choose any four consecutive Fibonacci numbers. Add the first and last, and divide by two.
What do you notice? Can you explain it?
1, 1, 2, 3 – 2
5,8,13,21 – 13
34,55,89,144 – 89
They are equal to the third term.
Add together any six consecutive Fibonacci numbers and divide by four.
What do you notice? Can you explain it?
1,1,2,3,5,8,=20/4=5
13,21,34,55,89,144= /5=89
Both of the previous questions’ answers are always equal to the second to the last term.
Can you discover any Fibonacci Surprises of your own?
Each term is calculated by adding together the previous two terms in the sequence.
-Adyan Ehtesham, Ahmed Sharafath, Ariel Justine Panopio
1+1+2=4 I noticed that the previous term's value is added to the next term.
ReplyDelete. 1+3=4/2=2 I notice that the answer is same as the third term.
. 1+1+2+3+5+8=20/4=5 I notice that the answer is same as the fifth term.
. No
1) The sun is even/double the largest number in the set of consecutive Fibonacci numbers. This is because the first two numbers equals the third number and double the third number equals an even number.
ReplyDeleteEx: a+b=c -> c=c -> c+c=2c (which is an even number)
2) The result would be the third number in the set.
Ex: a,b,c,d -> a+b=e* -> e/2=c
*In this case, 'e' can be denoted as 2c as well because it is the same as double of 'c'.
This happens because the sum of the first 3 numbers and the sum of the first and last numbers are the same, seeing as the sum of the second and the third numbers equals to the fourth/last multiple in the set.
Ex: a,b,c,d (where b+c=d) -> (a+b+c)/2 = (a+d)/2 -> c=c
3) The sum of the 6 consecutive Fibonacci numbers when divided by 4 is equals to the fifth number in the set.
Ex: (a+b+c+d+e+f)/2 = e
This is because:
-the third and fourth number equals the fifth number
-the first, second and sixth/last number equals to double the fifth number
-when all the sums are added together (including the fifth number as a separate result) then divided by 4, the answer is the fifth number in the set.
Ex: (a,b,c,d,e,f)
-c+d=e
-a+b+f=2e
2e+e+e= 4e
4e/4= e
4) Every third multiple of the Fibonacci sequence is an even number. Other than this fact, I haven't conjured up any other Fibonacci sequence by myself.
By Ma. Raphaela 8A