Secondary Math 1 Module 1 Sequences 1.8 Answer Key
Introduction
Welcome to our guide on the answer key for Secondary Math 1 Module 1 Sequences 1.8. In this article, we will provide a comprehensive answer key to help you understand and solve the sequences presented in the module. Sequences are an important concept in mathematics, as they allow us to study patterns and make predictions. By mastering the concepts covered in this module, you will develop a solid foundation for future math topics. So, let's dive in and explore the answer key for Secondary Math 1 Module 1 Sequences 1.8!
Understanding Sequences
Before we delve into the answer key, let's first understand what sequences are. In mathematics, a sequence is an ordered list of numbers, called terms, that follow a specific pattern. These patterns can be arithmetic, geometric, or even more complex. Sequences allow us to analyze and predict the behavior of numbers, making them a crucial concept in various fields of study.
Arithmetic Sequences
The first type of sequence we will discuss is arithmetic sequences. In an arithmetic sequence, each term is obtained by adding a common difference to the previous term. For example, the sequence 2, 5, 8, 11, 14, ... is an arithmetic sequence with a common difference of 3. To find the nth term of an arithmetic sequence, we use the formula: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, and d is the common difference.
Geometric Sequences
Next, let's explore geometric sequences. In a geometric sequence, each term is obtained by multiplying the previous term by a common ratio. For example, the sequence 2, 6, 18, 54, 162, ... is a geometric sequence with a common ratio of 3. To find the nth term of a geometric sequence, we use the formula: an = a1 * r^(n-1), where an is the nth term, a1 is the first term, and r is the common ratio.
Answer Key for Secondary Math 1 Module 1 Sequences 1.8
Question 1:
Find the common difference and write an equation for the arithmetic sequence: 5, 10, 15, 20, ...
Answer:
The common difference for this arithmetic sequence is 5. The equation for the nth term would be: an = 5n.
Question 2:
Find the common ratio and write an equation for the geometric sequence: 2, 4, 8, 16, ...
Answer:
The common ratio for this geometric sequence is 2. The equation for the nth term would be: an = 2^(n-1).
Question 3:
Find the 8th term of the arithmetic sequence: 3, 7, 11, 15, ...
Answer:
To find the 8th term of an arithmetic sequence, we can use the formula: an = a1 + (n-1)d. Plugging in the values, we get: a8 = 3 + (8-1)4 = 3 + 28 = 31.
Question 4:
Find the 6th term of the geometric sequence: 2, 6, 18, 54, ...
Answer:
To find the 6th term of a geometric sequence, we can use the formula: an = a1 * r^(n-1). Plugging in the values, we get: a6 = 2 * 3^(6-1) = 2 * 3^5 = 2 * 243 = 486.
Question 5:
Is the sequence 2, 4, 8, 16, ... arithmetic or geometric?
Answer:
The sequence 2, 4, 8, 16, ... is a geometric sequence with a common ratio of 2. Each term is obtained by multiplying the previous term by 2.
Question 6:
Is the sequence 3, 7, 11, 15, ... arithmetic or geometric?
Answer:
The sequence 3, 7, 11, 15, ... is an arithmetic sequence with a common difference of 4. Each term is obtained by adding 4 to the previous term.
Question 7:
Find the sum of the first 10 terms of the arithmetic sequence: 2, 5, 8, 11, ...
Answer:
To find the sum of the first 10 terms of an arithmetic sequence, we can use the formula: Sn = (n/2)(a1 + an). Plugging in the values, we get: S10 = (10/2)(2 + 29) = 5 * 31 = 155.
Question 8:
Find the sum of the first 5 terms of the geometric sequence: 3, 9, 27, 81, ...
Answer:
To find the sum of the first 5 terms of a geometric sequence, we can use the formula: Sn = a1 * (1 - r^n) / (1 - r). Plugging in the values, we get: S5 = 3 * (1 - 3^5) / (1 - 3) = 3 * (1 - 243) / (-2) = 3 * (-242) / (-2) = 363.
Question 9:
Find the missing term in the arithmetic sequence: 4, 7, _, 13, 16
Answer:
To find the missing term in an arithmetic sequence, we can analyze the common difference between consecutive terms. In this case, the common difference is 3. Therefore, the missing term is 10.
Question 10:
Find the missing term in the geometric sequence: 2, 4, _, 16, 32
Answer:
To find the missing term in a geometric sequence, we can analyze the common ratio between consecutive terms. In this case, the common ratio is 2. Therefore, the missing term is 8.
Conclusion
By completing this answer key for Secondary Math 1 Module 1 Sequences 1.8, you have gained a deeper understanding of arithmetic and geometric sequences. These concepts are fundamental in mathematics and will serve as building blocks for future topics. With this knowledge, you can confidently solve and analyze sequences, making predictions and drawing conclusions. Remember to practice regularly to reinforce these skills and explore more complex sequences in the world of mathematics!