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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: First, let's identify if the sequence is arithmetic or geometric. An arithmetic sequence has a common difference between consecutive terms, while a geometric sequence has a common ratio.To determine if it's arithmetic, we'll subtract the second term from the first term, and then the third term from the second term, and so on.
- Calculate first term difference: Subtract the first term from the second term: \(5x + ) - (x - ) = x + - x + = \
- Calculate second term difference: Subtract the second term from the third term: \(5x + ) - (x + ) = x + - x - = \
- Sequence type conclusion: Since the difference between consecutive terms is constant, we can conclude that the sequence is arithmetic. The common difference is .
