b Write out the eight ordered pairs before graphing them.
C
c Compare the value of the common difference to the slope.
A
a 5
B
b
C
c They are equal.
Practice makes perfect
a We have been asked to find the common difference of the arithmetic sequence. The common difference is the difference between the terms in the arithmetic sequence.
10 +5 ⟶ 15 +5 ⟶ 20 +5 ⟶ 25...
Since the terms are constantly increasing by 5, the common difference is 5.
b When creating our graph, we are asked to use the first eight terms of the sequence. To graph we will form ordered pairs by using the term values and the term numbers. Then, we will plot the points and draw a line through all of them. We will use the common difference found in Part A to find the terms.
10 +5 ⟶ 15 +5 ⟶ 20 +5 ⟶ &25
&↓ +5
45 +5 ⟵ 40 +5 ⟵ 35 +5 ⟵ &30Now that we have the first eight terms we can write the eight ordered pairs.
Term Number (x)
Term Value (y)
Ordered Pair (x,y)
1
10
(1,10)
2
15
(2,15)
3
20
(3,20)
4
25
(4,25)
5
30
(5,30)
6
35
(6,35)
7
40
(7,40)
8
45
(8,45)
We can plot these points and draw a line through them to have the graph of the sequence.
c We have been asked how the common difference of the sequence compares to the slope of the line. To do so, let's find the slope of the line.
Using the fact that slope is equal to rise over run, we can find the slope.
