A. Classify each sequence as arithmetic or geometric. Then, identify its common difference or ratio.
1) 5, 10, 20, 40, 80, ...
2),,,,... 4) 20 000, 1 000, 5 000, 2
3) 3,-21, 63, -189,...
500, ...
5) 7, 11, 15, 19, 23, ...
Answer:
Let's classify each sequence as either arithmetic or geometric and identify the common difference or ratio:
1) Sequence: 5, 10, 20, 40, 80, ...
- Classification: Geometric
- Common Ratio: Each term is multiplied by 2 to get the next term.
2) Sequence: 20,000, 1,000, 5,000, 2,500, ...
- Classification: Arithmetic
- Common Difference: Each term is obtained by dividing the previous term by 2.
3) Sequence: 3, -21, 63, -189, ...
- Classification: Arithmetic
- Common Difference: Each term is obtained by multiplying the previous term by -7.
4) Sequence: 500, ...
- Classification: Arithmetic
- Common Difference: There is not enough information to determine the common difference from the provided terms.
5) Sequence: 7, 11, 15, 19, 23, ...
- Classification: Arithmetic
- Common Difference: Each term is obtained by adding 4 to the previous term.
So, for the given sequences, the classifications and common differences/ratios are as follows:
1) Geometric with a common ratio of 2.
2) Arithmetic with a common difference of dividing by 2.
3) Arithmetic with a common difference of -7.
4) Arithmetic, but the common difference is not given.
5) Arithmetic with a common difference of 4.