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 $F_{4}, F_{6}, F_{8}, . . .$ . Using the notation $F_{2 n}$ for the Fibonnaci numbers in this set try to write down a general fomrmula for $F_{2 n}$ in terms of $F_{n + 1}$ and $F_{n - 1}$ .

The second set is $F_{3}, F_{5}, F_{7}, . . .$ . Using $F_{2 n + 1}$ for the Fibonacci numbers in this set try to write down a general formula for $F_{2 n + 1}$ in terms of $F_{n}$ and $F_{n + 1}$ .