Arithmetic Series -Mathematics- Grade 10

Arithmetic Series

1. Welcome to our Math Class!

2. Find the sum of the following: 1 + 2 + 3 + 4 + 5 + 6 b) 5 + 10 + 15 + 20 +25 c) 1 + 4 +7 + . . . . + 31

3.  the sum of a sequence in which each term is computed from the previous one by adding (or subtracting) a constant. Arithmetic Series

4. How do we compute the sum of all the terms of each of the following sequences? 1, 2, 3, . . . , 100 b) 5, 10, 15, 20, . . . , 50 c) −5, −2, 1, 4, . . . , 31

5. To find the sum of the terms of an arithmetic sequence, we can use the following formula: A. If the first and last terms are given: = ( + ) where: is the sum of the first n terms is the first term is the last term  

6. Example: 1. Find the sum of the first 20 natural numbers. 2. Find the sum of all the terms of the sequence: 5, 10, 15, 20, ..., 50. 3. Find the sum −5, −2 , 1, 4,..., 31.

7. To find the sum of the terms of an arithmetic sequence, we can use the following formula: A. If the last terms is not given: = [2 + (n - 1)d ] where: is the sum of the first n terms is the first term d is the common difference  

8. Example: 1. Find the sum of the first 20 terms of the arithmetic sequence 15, 19, 23, 27, … 2. Find the sum of the first 15 terms of the arithmetic sequence 9, 12, 15, … 3. Find the sum −5, −2 , 1, 4,..., 31.

9. Find the sum of the following arithmetic sequence. 1. Find the sum of the integers between 1 and 70 that are divisible by 3. 2. Find the sum of all odd numbers from 1 to 99. 3. Find the sum of all the even numbers between 1 and 100

10. Solve the following: 1. If the first n terms of the sequence: 9, 12, 15, 18, ... are added, how many terms give a sum of 126? 2. The sum of the first 15 terms of an arithmetic sequence is 765. If the first term is 23, what is the common difference? 3. The sum of the first 12 terms of an arithmetic sequence is 606. What is the first term if the last term is 67?

11. Solve the following: 1. If the sum of the first 8 terms of an arithmetic sequence is 172 and its common difference is 3, what is the first term? 2. If the sum of the first 9 terms of an arithmetic sequence is 216 and its first term is 4, what is the common difference?