Answer
(a)
$a_1=7$
$a_2=10$
$a_3=13$
$a_4=16$
$a_5=19$
(b) $d=3$
(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:
$a_1=7+3(1-1) = 7+3(0) = 7+0=7$
$a_2=7+3(2-1) = 7+3(1) = 7+3=10$
$a_3=7+3((3-1) = 7+3(2) = 7+6=13$
$a_4=7+3((4-1) = 7+3(3) = 7+9=16$
$a_5=7+3((5-1) = 7+3(4) = 7+12=19$
(b) The common difference can be found by subtracting the first term to the second term:
$d=10-7
\\d=3$
(c) Plot the points:
$(1, 7)
\\(2, 10)
\\(3, 13)
\\(4. 16)
\\(5, 19)$
Refer to the attached image in the answer part above.