## Secondary Math 1 Module 1 Sequences 1.6 Answer Key

### Introduction

Secondary Math 1 is a comprehensive course that covers various mathematical concepts and skills. Module 1 focuses on sequences, which are ordered lists of numbers or terms. In this article, we will provide you with the answer key for Module 1 Sequences 1.6, which covers arithmetic sequences. By understanding the answer key, you will gain a deeper understanding of the concepts and be better prepared for assessments and exams.

### Arithmetic Sequences

Arithmetic sequences are sequences in which each term is obtained by adding a fixed number, called the common difference, to the previous term. The general form of an arithmetic sequence is represented as:

a_{n} = a_{1} + (n-1)d

where a_{n} is the nth term, a_{1} is the first term, n is the position of the term, and d is the common difference.

### Answer Key for Module 1 Sequences 1.6

### Question 1:

Find the 10th term of the arithmetic sequence with a first term of 3 and a common difference of 4.

Solution:

Using the formula a_{n} = a_{1} + (n-1)d, we can substitute the given values:

a_{10} = 3 + (10-1)4

a_{10} = 3 + 9 * 4

a_{10} = 3 + 36

a_{10} = 39

Therefore, the 10th term of the arithmetic sequence is 39.

### Question 2:

Find the common difference of the arithmetic sequence with a first term of -2 and a 7th term of 20.

Solution:

Using the formula a_{n} = a_{1} + (n-1)d, we can substitute the given values:

20 = -2 + (7-1)d

20 = -2 + 6d

22 = 6d

d = 22/6

d = 11/3

Therefore, the common difference of the arithmetic sequence is 11/3.

### Question 3:

Find the position of the term in the arithmetic sequence with a first term of 5 and a common difference of -2, if the term is -13.

Solution:

Using the formula a_{n} = a_{1} + (n-1)d, we can substitute the given values:

-13 = 5 + (n-1)(-2)

-13 = 5 - 2n + 2

-13 - 7 = -2n

-20 = -2n

n = -20 / -2

n = 10

Therefore, the position of the term in the arithmetic sequence is 10.

### Question 4:

Find the sum of the first 15 terms of the arithmetic sequence with a first term of 2 and a common difference of 3.

Solution:

Using the formula for the sum of an arithmetic series:

S_{n} = (n/2)(a_{1} + a_{n})

We can substitute the given values:

S_{15} = (15/2)(2 + a_{15})

S_{15} = (15/2)(2 + (15-1)3)

S_{15} = (15/2)(2 + 14 * 3)

S_{15} = (15/2)(2 + 42)

S_{15} = (15/2)(44)

S_{15} = 15 * 22

S_{15} = 330

Therefore, the sum of the first 15 terms of the arithmetic sequence is 330.

### Conclusion

Understanding arithmetic sequences is crucial in mastering the concepts of mathematics. By going through the answer key for Module 1 Sequences 1.6, you have gained a deeper understanding of arithmetic sequences and how to solve problems related to them. Remember to practice and apply these concepts in order to excel in your math studies.