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Questions and Answers
Which of the following terms completes the arithmetic sequence -1, -7, _____, -19, -25, …?
Which of the following terms completes the arithmetic sequence -1, -7, _____, -19, -25, …?
Which of the following sequences is an arithmetic sequence?
Which of the following sequences is an arithmetic sequence?
What is the common difference of an arithmetic sequence where $a_2 = 1$ and $a_5 = 7$?
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, …?
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, …?
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, … ?
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, …?
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?
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?
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?
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?
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?
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.
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?
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.
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?
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?
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?
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?
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?
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?
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?
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?
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 $a_5 = 14$?
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 $7p + 2, 5p + 12, 3p + 22, …$?
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, ...?
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?
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?
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, ...?
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?
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.
Studying That Suits You
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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.
