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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).
- Determine Sequence Type: First, let's determine whether the sequence is arithmetic or geometric. An arithmetic sequence has a constant difference between consecutive terms, while a geometric sequence has a constant ratio between consecutive terms. We will look at the differences between consecutive terms to check for an arithmetic sequence.
- Calculate st Difference: Calculate the difference between the first and second terms:
- Calculate nd Difference: Calculate the difference between the second and third terms:
- Confirm Arithmetic Sequence: Since the differences between consecutive terms are the same (), we can conclude that the sequence is arithmetic with a common difference of .
