Arithmetic Series Grade 10 Mathematics Q1
- 2. Learning Competency At the end of the lesson, the learners should be able to determine arithmetic means, nth term of an arithmetic sequence, and sum of the terms of a given arithmetic sequence.
- 3. Objectives At the end of this lesson, the learners should be able to do the following: ● Accurately differentiate an arithmetic series from arithmetic sequence. ● Correctly solve for the sum of the first terms of an arithmetic sequence. ● Correctly solve real-life problems involving arithmetic series.
- 4. Let us say that you are in a theater. You noticed that there are 15 seats in the first row, 16 on the second row, 17 on the third row, and so on, until the last row. How would you know how many chairs are there?
- 5. We can easily determine how many chairs are there through the use of arithmetic sequence. In this lesson, we will discuss about arithmetic series and its applications.
- 6. Essential Questions ● How will you determine the necessary variables needed to solve for the first terms of an arithmetic series? ● How will you solve for the sum of the first terms of an arithmetic series?
- 7. Learn about It! This refers to the sum of the first terms of an arithmetic sequence, written as . Arithmetic Series
- 8. Learn about It! Example: The sum of the first five terms of an arithmetic series is Arithmetic Series
- 9. Learn about It! The arithmetic series can be solved using the following formula. Sum of the First Terms of an Arithmetic Sequence If is given
- 10. Learn about It! Alternatively, another formula can be used to solve for the first terms of an arithmetic series. Sum of the First Terms of an Arithmetic Sequence If is not given
- 11. Learn about It! Example: The sum of the first ten positive integers can be solved using the arithmetic series. Given that , , and , it follows that Sum of the First Terms of an Arithmetic Sequence
- 12. Learn about It! Example: Sum of the First Terms of an Arithmetic Sequence
- 13. Try it! Let’s Practice Example 1: Find the sum of the terms of an arithmetic series given that , , and .
- 14. Solution to Let’s Practice Solution: In the given example, the variables , , and are given. We can use the formula to solve for the sum of the terms of the arithmetic series. Example 1: Find the sum of the terms of an arithmetic series given that , , and .
- 15. Solution to Let’s Practice Solution: Substituting , , and , we get Example 1: Find the sum of the terms of an arithmetic series given that , , and .
- 16. Solution to Let’s Practice Solution: Therefore, the sum of the terms of the given arithmetic series is . Example 1: Find the sum of the terms of an arithmetic series given that , , and .
- 17. Try it! Let’s Practice Example 2: Find the sum of the first 20 terms of the arithmetic sequence
- 18. Solution to Let’s Practice Solution: 1. Determine the necessary variables in the given arithmetic sequence. It can be observed that the first term of the sequence is . Also, since we would like to determine the sum of the first 20 terms of the arithmetic sequence, it follows that . Example 2: Find the sum of the first 20 terms of the arithmetic sequence
- 19. Solution to Let’s Practice Solution: Next, we should determine the common difference of the arithmetic sequence. This is obtained by subtracting the two consecutive terms of the sequence. Example 2: Find the sum of the first 20 terms of the arithmetic sequence
- 20. Solution to Let’s Practice Solution: Since and , it follows that Example 2: Find the sum of the first 20 terms of the arithmetic sequence
- 21. Solution to Let’s Practice Solution: 2. Determine the sum of the arithmetic series. Since we know that values of the variables , , and , then we can solve the sum of the first 20 terms of the arithmetic series using the formula on the next slide. Example 2: Find the sum of the first 20 terms of the arithmetic sequence
- 22. Solution to Let’s Practice Solution: 2. Determine the sum of the arithmetic series. Example 2: Find the sum of the first 20 terms of the arithmetic sequence
- 23. Solution to Let’s Practice Solution: Substitute , , and , we get Example 2: Find the sum of the first 20 terms of the arithmetic sequence
- 24. Solution to Let’s Practice Solution: Example 2: Find the sum of the first 20 terms of the arithmetic sequence
- 25. Solution to Let’s Practice Solution: Thus, the sum of the first 20 terms of the arithmetic sequence is . Example 2: Find the sum of the first 20 terms of the arithmetic sequence
- 26. Try It! Individual Practice: 1. Find the sum of the first 10 terms of the arithmetic sequence , , , , … 2. The 3rd term of an arithmetic sequence is and its 6th term is 9. Write the first 8 terms of the sequence and find its sum.
- 27. Try It! Group Practice: To be done in groups of two to five The drama club of a school will stage a benefit play for the victims of the recent typhoon. There are 20 rows of seats in the school auditorium: 25 seats are in the 1st row, 27 seats on the 2nd row, 29 seats on the 3rd row, and so on. If the club plans to give complimentary tickets on the last row, how many complimentary tickets will they give? How much is the seating capacity of the school auditorium?
- 28. Key Points ● An arithmetic series refers to the sum of the first terms of an arithmetic sequence, written as .
- 29. Key Points ●The sum of the first terms of an arithmetic sequence can be solved using the following formula:
- 30. Bibliography Pierce, Rod. (16 Jan 2018). "Arithmetic Sequences and Sums". Math Is Fun. Retrieved 18 Feb 2019 from http://www.mathsisfun.com/algebra/sequences-sums-arithmetic.html