At the end of this question, it suggests that you look at the shapes of the gnomons for the alternate Fibonacci numbers. What do you notice about the gnomons for 3, 8 and 21 etc. that is different from the gnomons for 5, 13 and 34 etc?

You can describe what you notice in words or using algebra.

The first set is F₄, F₆, F₈, .... Using the notation F_2n for the Fibonnaci numbers in this set try to write down a general fomrmula for F_2n in terms of F_n+1 and F_n-1.

The second set isF₃, F₅, F₇, .... Using F_2n+1 for the Fibonacci numbers in this set try to write down a general formula for F_2n+1 in terms of F_n and F_n+1.