40 Secondary Math 1 Module 1 Sequences 1.6 Answer Key

Arithmetic Sequence Practice Worksheet — from db-excel.com

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 = a₁ + (n-1)d

where a_n is the nth term, a₁ 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 = a₁ + (n-1)d, we can substitute the given values:

a₁₀ = 3 + (10-1)4

a₁₀ = 3 + 9 * 4

a₁₀ = 3 + 36

a₁₀ = 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 = a₁ + (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 = a₁ + (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)(a₁ + a_n)

We can substitute the given values:

S₁₅ = (15/2)(2 + a₁₅)

S₁₅ = (15/2)(2 + (15-1)3)

S₁₅ = (15/2)(2 + 14 * 3)

S₁₅ = (15/2)(2 + 42)

S₁₅ = (15/2)(44)

S₁₅ = 15 * 22

S₁₅ = 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.