AI tutor
Welcome to Bytelearn!
Let’s check out your problem:
What kind of sequence is this?Choices:(A) arithmetic(B) geometric(C) both(D) neither
Full solution
Q. What kind of sequence is this?Choices:(A) arithmetic(B) geometric(C) both(D) neither
- Check for Arithmetic Sequence: Let's first check if the sequence is an arithmetic sequence by determining if there is a common difference between consecutive terms. Given sequence: Are the consecutive differences in the sequence equal? , , . The consecutive differences in the sequence are equal and the common difference is .
- Check for Geometric Sequence: Now, let's check if the sequence is a geometric sequence by determining if there is a common ratio between consecutive terms. Given sequence: Are the ratios between consecutive terms in the sequence equal? , , . The sequence has a common ratio of .
- Arithmetic Sequence Definition: An arithmetic sequence is defined as a sequence with a constant difference between consecutive terms. Since the difference here is , it satisfies the definition of an arithmetic sequence.
- Geometric Sequence Definition: A geometric sequence is defined as a sequence with a constant ratio between consecutive terms. Since the ratio here is , it satisfies the definition of a geometric sequence.
- Sequence is Both Arithmetic and Geometric: Since the sequence satisfies the definitions of both an arithmetic and a geometric sequence, the correct answer is that the sequence is both arithmetic and geometric.
