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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).
- Sequence Pattern Analysis: To determine whether the sequence is arithmetic or geometric, we need to examine 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.
- Check Arithmetic Sequence: Let's first check if the sequence is arithmetic by subtracting the second term from the first term: . Then we subtract the third term from the second term: . Since is not equal to , the sequence is not arithmetic.
- Check Geometric Sequence: Now let's check if the sequence is geometric by dividing the second term by the first term: . Then we divide the third term by the second term: . Since both ratios are equal, the sequence is geometric with a common ratio of .
