For each example, determine whether the given pattern is an arithmetic sequence.
If so, then find the common difference, d.
Example 1
Example 2
Example 3
Example 4
The sequence is 5, 22, 39, 56, ... What is the common difference in this sequence?
d = 17
Subtract any two CONSECUTIVE numbers in the sequence. 22 – 5 = 17, 56 – 39 = 17;
17 is the common difference.
The sequence is 66, 59, 52, 45, 38, 31, ... What is the common difference in this sequence?
d = -7.
Subtract any two CONSECUTIVE numbers in the sequence. We expect d to be negative because the numbers in the sequence are decreasing.
31 – 38 = -7; 45 – 52 = -7
The sequence is 4, 2.5, 1, -0.5, -2, -3.5, ... What is the common difference in this sequence?
d = -1.5. Subtract any two CONSECUTIVE numbers in the sequence. We expect d to be negative because the numbers in the sequence are decreasing.
1 – 2.5 = -1.5
-2 – (-0.5) = -2 + 0.5 = -1.5. This is harder with negative numbers. Remember to change signs and add when subtracting a negative number.
The common difference is -1.5
An ancient civilization left a torn parchment showing this sequence.
What is the sequence? What is the common difference?
The sequence is 2, 6, 10, 14, ...
The common difference is 4.
