Answer
(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.