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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 whether 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: st Two Terms: Let's first check if the sequence is arithmetic by finding the difference between the first two terms: .
- Calculate Difference: nd & rd Terms: Now, let's check the difference between the second and third terms: .
- Confirm Arithmetic Sequence: Since the difference between consecutive terms is the same , the sequence is an arithmetic sequence with a common difference of .
- Skip Checking for Geometric Sequence: We do not need to check for a common ratio because we have already determined that the sequence is arithmetic, not geometric.
