Trick of the Day  Sum of Fibonacci
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Trick of the Day  Sum of Fibonacci
Sooooo
The next trick
To find the sum of a finite fibonacci sequence, simply do the following:
ex. 1  2, 5, 7, 12, 19, 31, 50
1. First of all, identify the sequence as a fibonacci sequence.
2. Then, find the next term in the sequence (In our case, it is 81 [31 + 50 = 81])
3. Add the resulting number to the last term of the sequence and remember the answer (131 in our
case since 50 + 81 = 131)
4. Then, subtract the second term of the sequence (In our case, 5) from the number (1315 = 126)
5. You have your answer!!!!!
2 + 5 + 7 + 12 + 19 + 31 + 50 = 126
Cool Beans!!!!!!!!!!!
Lets look at another example
ex. 2  2 + 1 + 3 + 4 + 7 + 11 + 18 + 29 + 47
1. First of all, identify the sequence as a fibonacci sequence.
2. Then, find the next term in the sequence (In our case, it is 76 [29 + 47 = 76])
3. Add the resulting number to the last term of the sequence and remember the answer (123 in our
case since 47 + 76 = 123)
4. Then, subtract the second term of the sequence (In our case, 1) from the number (1231 = 122)
5. You have your answer!!!!!
2 + 1 + 3 + 4 + 7 + 11 + 18 + 29 + 47 = 122
Nice!!!!
Now try some Practice Problems.....
1. 2 + 10 + 12 + 22 + 34
2. 1 + 1 + 2 + 3 + 5
3. 7 + 5 + 12 + 17 + 29 + 46 + 75
4. 5 + 1 + 6 + .... + 20
5. 121 + 100 + 321 + 421
6. 2 + 19 + 21 + 40 + 61 + 101 + 162 + 263 + 425
7. 69 + 1 + 70 + 71 + 141 + 212 + 353
8. 1 + 1 + 2 + 3 + 5 + 8 + 13 + 21 + 34 + 55
9. 10 + 11 + 21 + 32 + 53 + 85 + 138 + 223
10. 5 + 7 + 12 + 19 + 31 + 50 + 81 + 131 + 212 + 343
11. 1 + 1 + 2 + 3 + 5 + 8 + 13 + 21 + 34 + 55 + 89 + 144 + 233 + 377 + 610
The next trick
To find the sum of a finite fibonacci sequence, simply do the following:
ex. 1  2, 5, 7, 12, 19, 31, 50
1. First of all, identify the sequence as a fibonacci sequence.
2. Then, find the next term in the sequence (In our case, it is 81 [31 + 50 = 81])
3. Add the resulting number to the last term of the sequence and remember the answer (131 in our
case since 50 + 81 = 131)
4. Then, subtract the second term of the sequence (In our case, 5) from the number (1315 = 126)
5. You have your answer!!!!!
2 + 5 + 7 + 12 + 19 + 31 + 50 = 126
Cool Beans!!!!!!!!!!!
Lets look at another example
ex. 2  2 + 1 + 3 + 4 + 7 + 11 + 18 + 29 + 47
1. First of all, identify the sequence as a fibonacci sequence.
2. Then, find the next term in the sequence (In our case, it is 76 [29 + 47 = 76])
3. Add the resulting number to the last term of the sequence and remember the answer (123 in our
case since 47 + 76 = 123)
4. Then, subtract the second term of the sequence (In our case, 1) from the number (1231 = 122)
5. You have your answer!!!!!
2 + 1 + 3 + 4 + 7 + 11 + 18 + 29 + 47 = 122
Nice!!!!
Now try some Practice Problems.....
1. 2 + 10 + 12 + 22 + 34
2. 1 + 1 + 2 + 3 + 5
3. 7 + 5 + 12 + 17 + 29 + 46 + 75
4. 5 + 1 + 6 + .... + 20
5. 121 + 100 + 321 + 421
6. 2 + 19 + 21 + 40 + 61 + 101 + 162 + 263 + 425
7. 69 + 1 + 70 + 71 + 141 + 212 + 353
8. 1 + 1 + 2 + 3 + 5 + 8 + 13 + 21 + 34 + 55
9. 10 + 11 + 21 + 32 + 53 + 85 + 138 + 223
10. 5 + 7 + 12 + 19 + 31 + 50 + 81 + 131 + 212 + 343
11. 1 + 1 + 2 + 3 + 5 + 8 + 13 + 21 + 34 + 55 + 89 + 144 + 233 + 377 + 610
Last edited by Ani on Tue Feb 24, 2009 6:22 pm; edited 1 time in total
Ani VicePresident
 Number of posts : 236
Age : 26
Location : Kanto
Registration date : 20080502
Re: Trick of the Day  Sum of Fibonacci
Ani wrote:
(121 in our case since 47 + 76 = 121)
I assume you meant 123 by 121?
Grant VicePresident
 Number of posts : 28
Age : 25
Location : Somewhere
Registration date : 20080905
Re: Trick of the Day  Sum of Fibonacci
Grant wrote:Ani wrote:
(121 in our case since 47 + 76 = 121)
I assume you meant 123 by 121?
Yes, I'll change that
Ani VicePresident
 Number of posts : 236
Age : 26
Location : Kanto
Registration date : 20080502
Re: Trick of the Day  Sum of Fibonacci
It was definitely not fun figuring that trick out by myself. >_<
Also, you could have simply said "find the next next term" or "find the second term after the sequence." However, good work. Carry on.
Also, you could have simply said "find the next next term" or "find the second term after the sequence." However, good work. Carry on.
HTang Graduated member
 Number of posts : 44
Registration date : 20090128
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