Chapter 8, Sequences and Series - Section 8.1 - Sequences and Summation Notation - 8.1 Exercises - Page 601: 76

$G_{1}=1$ $G_{2}=1$ $G_{3}=2$ $G_{4}=3$ $G_{5}=5$ $G_{6}=8$ $G_{7}=13$ $G_{8}=21$ $G_{9}=34$ $G_{10}=55$ Similar to Fibonacci sequence.

We are given: $G_n=\frac{1}{\sqrt{5}}(\frac{(1+\sqrt{5})^n-(1-\sqrt{5})^n}{2^n})$ We evaluate using a calculator: $G_{1}=1$ $G_{2}=1$ $G_{3}=2$ $G_{4}=3$ $G_{5}=5$ $G_{6}=8$ $G_{7}=13$ $G_{8}=21$ $G_{9}=34$ $G_{10}=55$ We compare to the Fibonacci sequence: $0, 1, 1, 2, 3, 5, 8, 13, 21, 34$... And we see that we get the same values.