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

Ani wrote:
(121 in our case since 47 + 76 = 121)

I assume you meant 123 by 121?

Grant wrote:

Ani wrote:
(121 in our case since 47 + 76 = 121)

I assume you meant 123 by 121?

Yes, I'll change that

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.