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.
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.