Certainly! Let's break down the sequences given in detail. Here are the three sequences that we need to analyze:
### Sequence 1
Given the sequence:
[tex]\[ -\frac{9}{11}, -\frac{2}{3}, -\frac{7}{13}, -\frac{3}{7}, -\frac{1}{3} \][/tex]
Let's convert these fractions into their decimal equivalents:
- [tex]\(-\frac{9}{11} \approx -0.8181\)[/tex]
- [tex]\(-\frac{2}{3} \approx -0.6667\)[/tex]
- [tex]\(-\frac{7}{13} \approx -0.5385\)[/tex]
- [tex]\(-\frac{3}{7} \approx -0.4286\)[/tex]
- [tex]\(-\frac{1}{3} \approx -0.3333\)[/tex]
So, the decimal form of Sequence 1 is:
[tex]\[ [-0.8181, -0.6667, -0.5385, -0.4286, -0.3333] \][/tex]
### Sequence 2
Given the sequence:
[tex]\[ \frac{5}{33}, \frac{5}{39}, \frac{10}{41}, \frac{2}{21} \][/tex]
Let's convert these fractions into their decimal equivalents:
- [tex]\(\frac{5}{33} \approx 0.1515\)[/tex]
- [tex]\(\frac{5}{39} \approx 0.1282\)[/tex]
- [tex]\(\frac{10}{41} \approx 0.2439\)[/tex]
- [tex]\(\frac{2}{21} \approx 0.0952\)[/tex]
So, the decimal form of Sequence 2 is:
[tex]\[ [0.1515, 0.1282, 0.2439, 0.0952] \][/tex]
### Sequence 3
Given the sequence:
[tex]\[ -\frac{10}{429}, -\frac{5}{273}, -\frac{4}{273} \][/tex]
Let's convert these fractions into their decimal equivalents:
- [tex]\(-\frac{10}{429} \approx -0.0233\)[/tex]
- [tex]\(-\frac{5}{273} \approx -0.0183\)[/tex]
- [tex]\(-\frac{4}{273} \approx -0.0147\)[/tex]
So, the decimal form of Sequence 3 is:
[tex]\[ [-0.0233, -0.0183, -0.0147] \][/tex]
### Summary
- Sequence 1 in decimal form is:
[tex]\[ [-0.8181, -0.6667, -0.5385, -0.4286, -0.3333] \][/tex]
- Sequence 2 in decimal form is:
[tex]\[ [0.1515, 0.1282, 0.2439, 0.0952] \][/tex]
- Sequence 3 in decimal form is:
[tex]\[ [-0.0233, -0.0183, -0.0147] \][/tex]
These decimal values are the step-by-step conversions from the provided fractions.
