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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 the type of sequence we are dealing with by examining the first few terms.The sequence given is To determine if it's an arithmetic sequence, we look for a common difference by subtracting each term from the one that follows it.Common difference
- Find Common Difference: Now, let's perform the subtraction to find the common difference.This means that the sequence is decreasing by each time, which indicates that it is an arithmetic sequence.
- Check Next Term: To confirm that this is indeed an arithmetic sequence, we should check if the same common difference applies to the next term in the sequence.We expect the third term to be the second term minus the common difference.Expected third term = second term - common difference =
- Calculate Expected Third Term: Let's calculate the expected third term.Expected third term = However, the actual third term given in the sequence is , not . This indicates that we have made a mistake in our calculations.
