Try This! Which of the following is an arithmetic sequence? 1) 1, 2, 3, 5, 7, 9, ... 2) 11, 12.5, 14, 15.5, ... 3) 1, -1, -3, -5, ... 4) 7, -7, 7, -7, ...
Answer (1)
An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is always the same. This difference is known as the common difference.
Let's examine each option to determine if it is an arithmetic sequence:
1, 2, 3, 5, 7, 9, ...
Checking the differences: 2 - 1 = 1, 3 - 2 = 1, 5 - 3 = 2.
The common difference is not consistent because 5 - 3 = 2 differs from the earlier differences.
This is not an arithmetic sequence.
11, 12.5, 14, 15.5, ...
Checking the differences: 12.5 - 11 = 1.5, 14 - 12.5 = 1.5, 15.5 - 14 = 1.5.
The common difference is consistent and equals 1.5.
This is an arithmetic sequence.
1, -1, -3, -5, ...
Checking the differences: -1 - 1 = -2, -3 - (-1) = -2, -5 - (-3) = -2.
The common difference is consistent and equals -2.
This is an arithmetic sequence.
7, -7, 7, -7, ...
Checking the differences: -7 - 7 = -14, 7 - (-7) = 14, -7 - 7 = -14.
The differences alternate between -14 and 14, which is not consistent.
This is not an arithmetic sequence.
Based on this analysis, options 2 and 3 are arithmetic sequences. If only one option needs to be selected, and considering typical multiple-choice formatting, option 2, 11, 12.5, 14, 15.5, ... , is the most straightforward example of an arithmetic sequence.
