Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Experience the ease of finding accurate answers to your questions from a knowledgeable community of professionals. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
To determine the type of each sequence, we need to analyze them one by one. We'll identify if each sequence is arithmetic, geometric, or neither.
1. First sequence: \( 3, 5, 7, 9, 11, \ldots \)
To check if this sequence is arithmetic, we need to see if there is a common difference between consecutive terms:
- \( 5 - 3 = 2 \)
- \( 7 - 5 = 2 \)
- \( 9 - 7 = 2 \)
- \( 11 - 9 = 2 \)
Since the difference is constant, this sequence is an arithmetic sequence.
2. Second sequence: \( \frac{1}{3}, \frac{1}{9}, \frac{1}{27}, \frac{1}{81}, \frac{1}{243}, \ldots \)
To check if this sequence is geometric, we need to see if there is a common ratio between consecutive terms:
- \( \frac{\frac{1}{9}}{\frac{1}{3}} = \frac{1}{9} \times \frac{3}{1} = \frac{1}{3} \)
- \( \frac{\frac{1}{27}}{\frac{1}{9}} = \frac{1}{27} \times \frac{9}{1} = \frac{1}{3} \)
- \( \frac{\frac{1}{81}}{\frac{1}{27}} = \frac{1}{81} \times \frac{27}{1} = \frac{1}{3} \)
- \( \frac{\frac{1}{243}}{\frac{1}{81}} = \frac{1}{243} \times \frac{81}{1} = \frac{1}{3} \)
Since the ratio is constant, this sequence is a geometric sequence.
3. Third sequence: \( 4, 20, 100, 500, 2500, \ldots \)
Let's check for a common ratio:
- \( \frac{20}{4} = 5 \)
- \( \frac{100}{20} = 5 \)
- \( \frac{500}{100} = 5 \)
- \( \frac{2500}{500} = 5 \)
Since the ratio is constant, this sequence is a geometric sequence.
4. Fourth sequence: \( \frac{25}{4}, \frac{5}{2}, 1, \frac{2}{5}, \frac{4}{25}, \ldots \)
Checking for common ratios:
- \( \frac{\frac{5}{2}}{\frac{25}{4}} = \frac{5}{2} \times \frac{4}{25} = \frac{20}{50} = \frac{2}{5} \)
- \( \frac{1}{\frac{5}{2}} = 1 \times \frac{2}{5} = \frac{2}{5} \)
- \( \frac{\frac{2}{5}}{1} = \frac{2}{5} \)
- \( \frac{\frac{4}{25}}{\frac{2}{5}} = \frac{4}{25} \times \frac{5}{2} = \frac{20}{50} = \frac{2}{5} \)
Since the ratio is not constant when checking further, this sequence is neither arithmetic nor geometric.
5. Fifth sequence: \( 5, -13, -29, -40, -59, \ldots \)
To check if this sequence is arithmetic:
- \( -13 - 5 = -18 \)
- \( -29 - (-13) = -29 + 13 = -16 \)
- \( -40 - (-29) = -40 + 29 = -11 \)
Since the difference is not constant, the sequence is not arithmetic.
Based on this analysis, the sequence types are:
1. Arithmetic (A)
2. Geometric (G)
3. Geometric (G)
4. Neither (N)
5. Arithmetic (A)
The correct string of letters describing each sequence is AGGNA.
1. First sequence: \( 3, 5, 7, 9, 11, \ldots \)
To check if this sequence is arithmetic, we need to see if there is a common difference between consecutive terms:
- \( 5 - 3 = 2 \)
- \( 7 - 5 = 2 \)
- \( 9 - 7 = 2 \)
- \( 11 - 9 = 2 \)
Since the difference is constant, this sequence is an arithmetic sequence.
2. Second sequence: \( \frac{1}{3}, \frac{1}{9}, \frac{1}{27}, \frac{1}{81}, \frac{1}{243}, \ldots \)
To check if this sequence is geometric, we need to see if there is a common ratio between consecutive terms:
- \( \frac{\frac{1}{9}}{\frac{1}{3}} = \frac{1}{9} \times \frac{3}{1} = \frac{1}{3} \)
- \( \frac{\frac{1}{27}}{\frac{1}{9}} = \frac{1}{27} \times \frac{9}{1} = \frac{1}{3} \)
- \( \frac{\frac{1}{81}}{\frac{1}{27}} = \frac{1}{81} \times \frac{27}{1} = \frac{1}{3} \)
- \( \frac{\frac{1}{243}}{\frac{1}{81}} = \frac{1}{243} \times \frac{81}{1} = \frac{1}{3} \)
Since the ratio is constant, this sequence is a geometric sequence.
3. Third sequence: \( 4, 20, 100, 500, 2500, \ldots \)
Let's check for a common ratio:
- \( \frac{20}{4} = 5 \)
- \( \frac{100}{20} = 5 \)
- \( \frac{500}{100} = 5 \)
- \( \frac{2500}{500} = 5 \)
Since the ratio is constant, this sequence is a geometric sequence.
4. Fourth sequence: \( \frac{25}{4}, \frac{5}{2}, 1, \frac{2}{5}, \frac{4}{25}, \ldots \)
Checking for common ratios:
- \( \frac{\frac{5}{2}}{\frac{25}{4}} = \frac{5}{2} \times \frac{4}{25} = \frac{20}{50} = \frac{2}{5} \)
- \( \frac{1}{\frac{5}{2}} = 1 \times \frac{2}{5} = \frac{2}{5} \)
- \( \frac{\frac{2}{5}}{1} = \frac{2}{5} \)
- \( \frac{\frac{4}{25}}{\frac{2}{5}} = \frac{4}{25} \times \frac{5}{2} = \frac{20}{50} = \frac{2}{5} \)
Since the ratio is not constant when checking further, this sequence is neither arithmetic nor geometric.
5. Fifth sequence: \( 5, -13, -29, -40, -59, \ldots \)
To check if this sequence is arithmetic:
- \( -13 - 5 = -18 \)
- \( -29 - (-13) = -29 + 13 = -16 \)
- \( -40 - (-29) = -40 + 29 = -11 \)
Since the difference is not constant, the sequence is not arithmetic.
Based on this analysis, the sequence types are:
1. Arithmetic (A)
2. Geometric (G)
3. Geometric (G)
4. Neither (N)
5. Arithmetic (A)
The correct string of letters describing each sequence is AGGNA.
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.
