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For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).
Full solution
Q. For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).
- Identify Pattern: To determine if the sequence is arithmetic or geometric, we need to look at the pattern of the numbers. In an arithmetic sequence, the difference between consecutive terms is constant. In a geometric sequence, the ratio between consecutive terms is constant.
- Calculate Difference : Let's check the difference between the first two terms: .
- Calculate Difference : Now, let's check the difference between the second and third terms: .
- Confirm Arithmetic Sequence: Since the difference between consecutive terms is constant, we can conclude that the sequence is an arithmetic sequence with a common difference of .
- Eliminate Incorrect Options: We can ignore the options and , as they do not represent the common difference we found. The options and are left, and since we determined the common difference is positive, is not the correct answer.
