College Algebra 7th Edition

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

Chapter 8, Sequences and Series - Section 8.2 - Arithmetic Sequences - 8.2 Exercises - Page 607: 10

Answer

(a) $a_1=0$ $a_2=\frac{1}{2}$ $a_3=1$ $a_4=\frac{3}{2}$ $a_5=2$ (b) $d=\frac{1}{2}$ (c) Refer to the image below for the graph.
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Work Step by Step

(a) Find the first five terms of the sequence by substituting 1, 2, 3, 4, and 5 to the given formula to obtain: $a_1=\frac{1}{2}(1-1) = \frac{1}{2}(0)=0$ $a_2=\frac{1}{2}(2-1) = \frac{1}{2}(1)=\frac{1}{2}$ $a_3=\frac{1}{2}(3-1) = \frac{1}{2}(2)=1$ $a_4=\frac{1}{2}(4-1) = \frac{1}{2}(3)=\frac{3}{2}$ $a_5=\frac{1}{2}(5-1) = \frac{1}{2}(4)=2$ (b) The common difference can be found by subtracting the first term to the second term: $d=\frac{1}{2} - 0 \\d=\frac{1}{2}$ (c) Plot the points: $(1, 0) \\(2, \frac{1}{2}) \\(3, 1) \\(4, \frac{3}{2}) \\(5, 2)$ Refer to the attached image in the answer part above.
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