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 Arithmetic Sequence: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. Given sequence: Calculate the differences: , , .
- Verify Common Difference: Since the differences between consecutive terms are equal, this suggests that the sequence could be an arithmetic sequence. In an arithmetic sequence, each term after the first is obtained by adding a constant, called the common difference, to the previous term.
- Check Geometric Sequence: Now, let's verify if the sequence could also be geometric by checking if there is a common ratio between consecutive terms. Calculate the ratios: , , .
- Calculate Ratios: Perform the calculations: , , . The ratios are not equal.
- Sequence Not Geometric: Since the ratios between consecutive terms are not equal, the sequence is not geometric. A geometric sequence requires a common ratio between all consecutive terms.
- Conclusion: Based on the calculations, we can conclude that the sequence is arithmetic because it has a common difference, but it is not geometric because it does not have a common ratio.
