At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
To determine which of the given series is a geometric series, we need to examine the ratios between consecutive terms in each series. A series is geometric if the ratio between successive terms is constant.
Let's analyze each series one by one:
1. The series [tex]\(6, 13, 20, 27\)[/tex]:
[tex]\[ \frac{13}{6} \approx 2.167, \quad \frac{20}{13} \approx 1.538, \quad \frac{27}{20} = 1.35 \][/tex]
The ratios are not consistent, so this is not a geometric series.
2. The series [tex]\(7, 21, 35, 45\)[/tex]:
[tex]\[ \frac{21}{7} = 3, \quad \frac{35}{21} \approx 1.667, \quad \frac{45}{35} \approx 1.286 \][/tex]
The ratios are not consistent, so this is not a geometric series.
3. The series [tex]\(14, 21, 28, 35\)[/tex]:
[tex]\[ \frac{21}{14} = 1.5, \quad \frac{28}{21} \approx 1.333, \quad \frac{35}{28} = 1.25 \][/tex]
The ratios are not consistent, so this is not a geometric series.
4. The series [tex]\(2, 14, 98, 686\)[/tex]:
[tex]\[ \frac{14}{2} = 7, \quad \frac{98}{14} = 7, \quad \frac{686}{98} = 7 \][/tex]
The ratios are consistent and equal to 7, so this is a geometric series.
Hence, the series that forms a geometric progression is:
[tex]\[ 2, 14, 98, 686 \][/tex]
Let's analyze each series one by one:
1. The series [tex]\(6, 13, 20, 27\)[/tex]:
[tex]\[ \frac{13}{6} \approx 2.167, \quad \frac{20}{13} \approx 1.538, \quad \frac{27}{20} = 1.35 \][/tex]
The ratios are not consistent, so this is not a geometric series.
2. The series [tex]\(7, 21, 35, 45\)[/tex]:
[tex]\[ \frac{21}{7} = 3, \quad \frac{35}{21} \approx 1.667, \quad \frac{45}{35} \approx 1.286 \][/tex]
The ratios are not consistent, so this is not a geometric series.
3. The series [tex]\(14, 21, 28, 35\)[/tex]:
[tex]\[ \frac{21}{14} = 1.5, \quad \frac{28}{21} \approx 1.333, \quad \frac{35}{28} = 1.25 \][/tex]
The ratios are not consistent, so this is not a geometric series.
4. The series [tex]\(2, 14, 98, 686\)[/tex]:
[tex]\[ \frac{14}{2} = 7, \quad \frac{98}{14} = 7, \quad \frac{686}{98} = 7 \][/tex]
The ratios are consistent and equal to 7, so this is a geometric series.
Hence, the series that forms a geometric progression is:
[tex]\[ 2, 14, 98, 686 \][/tex]
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.