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What kind of sequence is this?Choices:(A) arithmetic(B) geometric(C) both(D) neither
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Q. What kind of sequence is this?Choices:(A) arithmetic(B) geometric(C) both(D) neither
- Verify Consecutive Differences Uniform: Let's verify if the differences between consecutive terms are uniform. Given sequence: Are the consecutive differences in the sequence equal? , , .The consecutive differences in the sequence are equal and the common difference is .
- Check Arithmetic Sequence Definition: Since the sequence has a common difference, it could be an arithmetic sequence. Let's check the definition.Arithmetic sequence: A sequence in which each term after the first is obtained by adding a constant difference to the preceding term.Given sequence: The sequence fits the definition of an arithmetic sequence.
- Check Geometric Sequence Ratios: Now, let's check if the sequence could also be a geometric sequence by verifying if the ratios between consecutive terms are equal.Given sequence: Are the ratios between consecutive terms in the sequence equal? , , .The ratios between consecutive terms are not equal, so the sequence does not have a common ratio.
- Confirm Not Geometric Sequence: Geometric sequence: A sequence in which each term after the first is obtained by multiplying the preceding term by a fixed, non-zero number called the common ratio.Given sequence: Since the sequence does not have a common ratio, it is not a geometric sequence.
