We are given the first term and the common difference of the arithmetic sequence A, and we are asked to find the common difference of the arithmetic sequence B, knowing that the graphs are parallel. Let's find some terms of A.
Term
Rule
Value
A(1)
-
3
A(2)
A(1)+2
5
A(3)
A(2)+2
7
A(4)
A(3)+2
9
By plotting the points, we can draw the graph of A. Let's also draw a line passing through these points.
Now, let's substitute 1 for n in the formula of B to find the value of its first term.
Let's now draw a parallel line passing through the point (1,5).
By looking at the graph, we can see that B(2)=7. This allows us to find the common difference of sequence B.
Common Difference: 7-5=2
What did we just learn? If the graphs of two arithmetic sequences are parallel, then they have the same common difference!
Alternative Solution
Slope and Common Difference
The common difference of an arithmetic sequence is also the slope of the line. The common difference of the first sequence is 2, and therefore the slope of the line that represents this sequence is also 2. Since the graphs of the sequences are parallel, the slope of the second line, and therefore, the common difference of the second sequence, is 2.
