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Questions and Answers
Which of the following terms completes the arithmetic sequence -1, -7, _____, -19, -25, …?
Which of the following sequences is an arithmetic sequence?
What is the common difference of an arithmetic sequence where $a_2 = 1$ and $a_5 = 7$?
Which term represents the first positive term of the arithmetic sequence -8, -6, -4, …?
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Which of the following is not true about the arithmetic sequence 5, 3, 1, -1, -3, …?
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Which of the following represents the common difference of the arithmetic sequence 3a -1, 3a, 3a + 1, … ?
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What is the common difference of the arithmetic sequence -1, -8, -15, -22, …?
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What is the common difference of the arithmetic sequence 24, 14, 4?
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What are the next three terms in the arithmetic sequence 6, 10, 14?
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What is the value of 'a' that makes the sequence 3a + 1, 4a, 6a + 1 an arithmetic sequence?
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What distance did the person walk on the 10th day if the pattern continues as 40m, 60m, 80m?
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What is the common difference of the sequence -7, 4, 15?
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Identify the common difference in the arithmetic sequence 21, 15, 9.
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What are the next three terms for the sequence 5, -1, -7?
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Determine the next three terms in the sequence 4.1, 11.1, 18.1.
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What is the common difference of the arithmetic sequence given by the terms 5, 3, 1, -1, and -3?
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Given that in the arithmetic sequence where 𝑎2 = 1 and 𝑎5 = 7, what value do we find for the common difference 𝑑?
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What is the first term of the arithmetic sequence if the fifth term is 7 and the common difference is 2?
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From the arithmetic sequence 3a - 1, 3a, 3a + 1, what is the expression for the common difference 𝑑?
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What is the fourth term of the arithmetic sequence with first term 5 and common difference -2?
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If 𝑎4 = 2 and the common difference is -1 in an arithmetic sequence, what is the value of 𝑎1?
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What represents the difference between the second term and the first term of an arithmetic sequence?
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Which of the following is an arithmetic sequence?
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What is the common difference of the arithmetic sequence if $a_3 = 4$ and $a_5 = 14$?
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What is the common difference of the arithmetic sequence $7p + 2, 5p + 12, 3p + 22, …$?
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What is the first positive term of the arithmetic sequence: -11, -8, -5, ...?
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Which value of p ensures that the terms $7p + 2, 5p + 12, 2p – 1,…$ form an arithmetic sequence?
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Which of the following sets is NOT an arithmetic sequence?
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Which is NOT true about the arithmetic sequence: 25, 32, 39, 46, ...?
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How many feet will the skydiver have jumped during the tenth fall, given he jumps 36, 48, and 60 feet in the first three falls?
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Study Notes
Arithmetic Sequence Overview
- An arithmetic sequence consists of numbers with a constant difference between consecutive terms.
- The common difference (d) can be found by subtracting one term from the subsequent term.
Identifying Common Difference
- For a sequence like 4, 7, 10, 13, the common difference is 3 (7-4=3).
- In the sequence -4, 3, 10, 17, the common difference is 7 (3 - (-4) = 7).
- The missing term in -1, -7, __, -19, -25 can be determined using the common difference -6.
Example Sequences
- The sequence 1, 1, 1, 1, 2 has a common difference of 0 initially, then changes.
- A sequence is arithmetic if the difference between terms is consistent, e.g., -8, -6, -4 (common difference of 2).
Specific Examples and Solutions
- For the sequence 3a - 1, 3a, 3a + 1, the common difference is 1.
- The sequence -11, -8, -5 continues with a common difference of 3 and the first positive term is -2.
- To make 3a + 1, 4a, 6a + 1 arithmetic, the value of a must be -2.
Real-Life Applications
- Walking pattern example: 40m, 60m, 80m indicates a daily increase of 20m; on the 10th day, 220m would be walked.
- In the skydiving scenario, where jumps increase by a pattern of 12 feet, the jump on the tenth fall would measure 132 feet.
Assessment of Arithmetic Sequences
- Sequences such as 25, 32, 39, 46 have a common difference of 7.
- Non-arithmetic sequences like 3, 9, 27, 81 do not have a constant difference.
Tasks for Practice
- Find the common difference for given sequences and predict the next three terms.
- Identify whether various sequences presented are arithmetic, providing justification for each case.
Summary Challenges
- Determine values for unknowns in arithmetic sequences based on given terms.
- Assess which provided sequences are not arithmetic and explain reasoning behind the classification.
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Description
This quiz covers the concepts related to illustrating arithmetic sequences as taught in Quarter I, Module 2 for Grade 10 Mathematics. Students will engage with key definitions, examples, and applications of arithmetic sequences. Assess your understanding and mastery of this important mathematical topic.
