Sum of sequence

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Sum of sequence

Postby 16422 » Wed Apr 17, 2013 9:49 pm

1 + 2 + 5 + 13 + ... + 89 + 233 = ____________

Aren't the differences between the terms the odd fibonacci numbers? So, +1, +3, +8, +21, +55, +144.
How do add this sequence without summing it up in your head?
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Re: Sum of sequence

Postby 16422 » Wed Apr 17, 2013 9:57 pm

And also this one:

5+7+12+19+31+ ... +131+212= ________________


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Re: Sum of sequence

Postby Fredfredburger » Wed Apr 17, 2013 10:06 pm

For the first one, the sum of the sequence of the odd fibonacci terms is simply the next term after the last term. Here the term after 233 is 377(233+144), your sum.

For the second it's is a fibonacci type sequence. The sum of a fibonacci sequence is the 2nd term after the last one you have minus the second term.

Here the first term after is 131+212=343

The second term is 343+212=555

555-7=548
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