AI tutor
Welcome to Bytelearn!
Let’s check out your problem:
Elizabeth sent e-mails on Tuesday, e-mails on Wednesday, e-mails on Thursday, and e-mails on Friday. What kind of sequence is this?Choices:(A) arithmetic(B) geometric(C) both(D) neither
Full solution
Q. Elizabeth sent e-mails on Tuesday, e-mails on Wednesday, e-mails on Thursday, and e-mails on Friday. What kind of sequence is this?Choices:(A) arithmetic(B) geometric(C) both(D) neither
- Examine Pattern of Numbers: To determine the type of sequence, we need to examine the pattern of numbers. An arithmetic sequence has a common difference between terms, while a geometric sequence has a common ratio. Let's check for a common difference first.We calculate the differences between consecutive terms:Difference between Wednesday and Tuesday: Difference between Thursday and Wednesday: Difference between Friday and Thursday:
- Calculate Differences: Now let's check if the differences form a pattern that indicates an arithmetic sequence. If the differences are not constant, it is not an arithmetic sequence.Comparing the differences: (from Tuesday to Wednesday) is not equal to (from Wednesday to Thursday), which is not equal to (from Thursday to Friday).Since the differences are not constant, this is not an arithmetic sequence.
- Check for Arithmetic Sequence: Next, we check for a common ratio to determine if it's a geometric sequence. We calculate the ratios between consecutive terms:Ratio between Wednesday and Tuesday: Ratio between Thursday and Wednesday: Ratio between Friday and Thursday:
- Calculate Ratios: Now let's check if the ratios are constant, which would indicate a geometric sequence.Comparing the ratios: (from Tuesday to Wednesday) is equal to (from Wednesday to Thursday), which is equal to (from Thursday to Friday).Since the ratios are constant, this is a geometric sequence.
