College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

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

Answer

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

Work Step by Step

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.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.