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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 Examination: To determine whether the sequence is arithmetic or geometric, we need to examine the pattern of the numbers. An arithmetic sequence has a constant difference between consecutive terms, while a geometric sequence has a constant ratio between consecutive terms.
- Check Arithmetic Sequence: Let's check for an arithmetic sequence by finding the difference between the second term and the first term: .
- Calculate Differences: Now, let's check the difference between the third term and the second term: .
- Conclusion: Arithmetic Sequence: Since the difference between consecutive terms is constant, we can conclude that the sequence is arithmetic, not geometric. Therefore, the common difference is .
- Ignore Extra Numbers: We can ignore the other numbers provided as they are not part of the sequence. The sequence provided is , and we have determined it is an arithmetic sequence with a common difference of .
