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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 examine the pattern of the terms. For an arithmetic sequence, we subtract consecutive terms to find a common difference. For a geometric sequence, we divide consecutive terms to find a common ratio.
- Check Arithmetic Sequence: First, let's check if it's an arithmetic sequence by subtracting the second term from the first term: . Then, subtract the third term from the second term: . Since does not equal , the sequence is not arithmetic because the differences are not the same.
- Check Geometric Sequence: Now, let's check if it's a geometric sequence by dividing the second term by the first term: . Then, divide the third term by the second term: . Since both ratios are the same, the sequence is geometric with a common ratio of .
