# Chapter 8, Sequences and Series - Section 8.2 - Arithmetic Sequences - 8.2 Exercises: 9

(a) $a_1=\frac{5}{2}$ $a_2=\frac{3}{2}$ $a_3=\frac{1}{2}$ $a_4=-\frac{1}{2}$ $a_5=-\frac{3}{2}$ (b) $d=1$ (c) Refer to the image below for the graph.

#### 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: $a_1=\frac{5}{2}-(1-1) = \frac{5}{2}-0=\frac{5}{2}$ $a_2=\frac{5}{2}-(2-1) = \frac{5}{2}-1=\frac{5}{2}-\frac{2}{2}=\frac{3}{2}$ $a_3=\frac{5}{2}-(3-1) = \frac{5}{2}-2=\frac{5}{2}-\frac{4}{2}=\frac{1}{2}$ $a_4=\frac{5}{2}-(4-1) = \frac{5}{2}-3=\frac{5}{2}-\frac{6}{2}=-\frac{1}{2}$ $a_5=\frac{5}{2}-(5-1) = \frac{5}{2}-4=\frac{5}{2}-\frac{8}{2}=-\frac{3}{2}$ (b) The common difference can be found by subtracting the first term to the second term: $d=\frac{3}{2} - \frac{5}{2} \\d=\frac{-2}{2} \\d=1$ (c) Plot the points: $(1, \frac{5}{2}) \\(2, \frac{3}{2}) \\(3, \frac{1}{2}) \\(4, -\frac{1}{2}) \\(5, \frac{3}{2})$ Refer to the attached image in the answer part above.

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