You are here:

Advanced Math/Sum of sequence


What is the sum of nth term of a sequence:
3, 4, 7, 11, 18, 29 .... nth (fibonacci)

Due to the difficulty of writing equations here, I've included links to illustrations.

The terms of your sequence are 3, 4, 7, 11, 18, 28, ...
If you compare this with the Fibonacci sequence, you'll see that
the nth term of this sequence is the sum of the nth and (n+2)th Fibonacci numbers.

Some facts about the Fibonacci sequence:
The nth term is (φⁿ - (1-φ)ⁿ/√5, where φ is the "golden ratio" (1+√5)/2.
The sum of the first n terms equals the (n+2)th term minus 1.

The sum of the first n terms of your sequence can be expressed in terms of the Fibonacci numbers:
  ∑t = [2(n+4)th number] - [(n+1)th number] - [(n+2)th number] - 4
which you can then calculate using φ. You can see the calculations here:
The final equation looks a fright!--but I have verified its accuracy in an Excel spreadsheet.  

Advanced Math

All Answers

Answers by Expert:

Ask Experts


Janet Yang


I can answer questions in Algebra, Basic Math, Calculus, Differential Equations, Geometry, Number Theory, and Word Problems. I would not feel comfortable answering questions in Probability and Statistics or Topology because I have not studied these in depth.


I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.

Co-author of An Outline of Scientific Writing: For Researchers With English as a Foreign Language

I have a Bachelor's degree in Applied Mathematics from the University of California at Berkeley.

Past/Present Clients
George White Elementary School. Homework Help program at the Ridgewood Public Library, Ridgewood, NJ. Individual students.

©2016 All rights reserved.