# Trick of the Day - Sum of Fibonacci

## 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 (131-5 = 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 (123-1 = 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 (131-5 = 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 (123-1 = 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**- Vice-President
- Number of posts : 236

Age : 25

Location : Kanto

Registration date : 2008-05-02

## 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**- Vice-President
- Number of posts : 28

Age : 24

Location : Somewhere

Registration date : 2008-09-05

## 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**- Vice-President
- Number of posts : 236

Age : 25

Location : Kanto

Registration date : 2008-05-02

## 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 : 2009-01-28

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