IDNLearn.com: Where your questions meet expert advice and community insights. Ask your questions and get detailed, reliable answers from our community of knowledgeable experts.
Sagot :
To determine which of the sequences is a geometric series, we need to check if the ratio between consecutive terms is constant for each series. Let's examine each sequence one by one.
1. Sequence: [tex]\(40, 50, 60, 70\)[/tex]
- Calculate the ratios between consecutive terms:
[tex]\( \frac{50}{40} = 1.25 \)[/tex]
[tex]\( \frac{60}{50} = 1.2 \)[/tex]
[tex]\( \frac{70}{60} = 1.1667 \)[/tex]
- The ratios are not the same, so this is not a geometric series.
2. Sequence: [tex]\(40, 42, 44, 46\)[/tex]
- Calculate the ratios between consecutive terms:
[tex]\( \frac{42}{40} = 1.05 \)[/tex]
[tex]\( \frac{44}{42} \approx 1.0476 \)[/tex]
[tex]\( \frac{46}{44} \approx 1.0455 \)[/tex]
- The ratios are not the same, so this is not a geometric series.
3. Sequence: [tex]\(40, 80, 40, 120\)[/tex]
- Calculate the ratios between consecutive terms:
[tex]\( \frac{80}{40} = 2 \)[/tex]
[tex]\( \frac{40}{80} = 0.5 \)[/tex]
[tex]\( \frac{120}{40} = 3 \)[/tex]
- The ratios are not the same, so this is not a geometric series.
4. Sequence: [tex]\(40, 20, 10, 5\)[/tex]
- Calculate the ratios between consecutive terms:
[tex]\( \frac{20}{40} = 0.5 \)[/tex]
[tex]\( \frac{10}{20} = 0.5 \)[/tex]
[tex]\( \frac{5}{10} = 0.5 \)[/tex]
- The ratios are the same (i.e., [tex]\(0.5\)[/tex]), hence this is a geometric series.
So, the geometric series among the given sequences is [tex]\(40, 20, 10, 5\)[/tex], making the correct answer:
[tex]\[ \boxed{4} \][/tex]
1. Sequence: [tex]\(40, 50, 60, 70\)[/tex]
- Calculate the ratios between consecutive terms:
[tex]\( \frac{50}{40} = 1.25 \)[/tex]
[tex]\( \frac{60}{50} = 1.2 \)[/tex]
[tex]\( \frac{70}{60} = 1.1667 \)[/tex]
- The ratios are not the same, so this is not a geometric series.
2. Sequence: [tex]\(40, 42, 44, 46\)[/tex]
- Calculate the ratios between consecutive terms:
[tex]\( \frac{42}{40} = 1.05 \)[/tex]
[tex]\( \frac{44}{42} \approx 1.0476 \)[/tex]
[tex]\( \frac{46}{44} \approx 1.0455 \)[/tex]
- The ratios are not the same, so this is not a geometric series.
3. Sequence: [tex]\(40, 80, 40, 120\)[/tex]
- Calculate the ratios between consecutive terms:
[tex]\( \frac{80}{40} = 2 \)[/tex]
[tex]\( \frac{40}{80} = 0.5 \)[/tex]
[tex]\( \frac{120}{40} = 3 \)[/tex]
- The ratios are not the same, so this is not a geometric series.
4. Sequence: [tex]\(40, 20, 10, 5\)[/tex]
- Calculate the ratios between consecutive terms:
[tex]\( \frac{20}{40} = 0.5 \)[/tex]
[tex]\( \frac{10}{20} = 0.5 \)[/tex]
[tex]\( \frac{5}{10} = 0.5 \)[/tex]
- The ratios are the same (i.e., [tex]\(0.5\)[/tex]), hence this is a geometric series.
So, the geometric series among the given sequences is [tex]\(40, 20, 10, 5\)[/tex], making the correct answer:
[tex]\[ \boxed{4} \][/tex]
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. IDNLearn.com provides the answers you need. Thank you for visiting, and see you next time for more valuable insights.