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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 Sequence Type: 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 Differences: Let's check the difference between the first two terms: . Now, let's check the difference between the second and third terms: . Since the difference is the same, it is an arithmetic sequence with a common difference of .
- Determine Correct Option: The options given are , , , and . Since we have determined that the sequence is arithmetic and the common difference is , the correct option is .
