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Questions and Answers
What is the difference between an arithmetic sequence and a geometric sequence?
What is the difference between an arithmetic sequence and a geometric sequence?
- The difference between successive terms is constant in an arithmetic sequence, while the ratio between successive terms is constant in a geometric sequence.
- Both arithmetic and geometric sequences have a constant difference between successive terms.
- The difference between successive terms is constant in a geometric sequence, while the ratio between successive terms is constant in an arithmetic sequence. (correct)
- Both arithmetic and geometric sequences have a constant ratio between successive terms.
What is the recursive definition for a geometric sequence with initial term a and common ratio r?
What is the recursive definition for a geometric sequence with initial term a and common ratio r?
- a_n = a_{n-1} - r; a_0 = a
- a_n = a_{n-1} + r; a_0 = a
- a_n = a_{n-1} / r; a_0 = a
- a_n = a_{n-1} * r; a_0 = a (correct)
If a sequence starts with a_1 instead of a_0, how can we find the term that would have been a_0?
If a sequence starts with a_1 instead of a_0, how can we find the term that would have been a_0?
- Add the common ratio to a_1.
- Subtract the common difference from a_1.
- Divide a_1 by the common difference.
- Subtract the first term from a_1 and divide the result by the common difference. (correct)
