LESSON #1 ARITHMETIC SEQUENCE GRADE 10.

GRADE 10 ARITHMETIC SEQUENCE

1. Lesson #1 ARITHMETIC SEQUENCE

2. ARITHMETIC SEQUENCE or NOT ARITHMETIC SEQUENCE

3. 4, 0, -4, -8, -12 ARITHMETIC SEQUENCE d = -4

4. 6.6, 7.2, 7.8, 8.4, 9,… ARITHMETIC SEQUENCE d = 0.6

5. 7 , 10, 16, 19, 25,… NOT ARITHMETIC SEQUENCE

6. 2, 4, 8, 10, 12, 16 NOT ARITHMETIC SEQUENCE

7. Directions: Solve the following problems involving arithmetic sequence. 1. Find the 50 th term of the sequence 5, –2, –9, –16, ...

8. A n = A 1 + (n-1) d A 50 = 5 + (50-1) (-7) A 50 = 5 + (49) (-7) A 50 = 5 + (-343) A 50 = -338 n = 50 A n = 50 th term A 1 = 5 d = -7

9. Directions: Solve the following problems involving arithmetic sequence. 2. What are the three next terms in the sequence with -23 as the first term and 2 as the common difference? A 1 = -23 d = 2 -23 + 2 = -21 -21 + 2 = -19 -19 + 2 = -17

10. Directions: Solve the following problems involving arithmetic sequence. 3. Yanna wants to save money to help her mother to pay her tuition fee. She decided to save Php 100.00 on April 1, Php 200.00 on April 2, Php 300.00 on April 3, and so on, how much did Yanna save on April 9? A 1 = 100 d = 100 n = 9 A n = A 1 + (n-1) d A 9 = 100 + (9-1) (100) A 9 = 100 + (8) (100) A 9 = 100 + 800 A 9 = 900 Php 900

11. 4. Cris is a working student at night who saves money for his future. He takes a job starting with an hourly wage of Php 3.50 and is promised a raise of Php 5.00 per hour every two months for 5 years. At the end of 5 years, what would be Cris ’ hourly wage? A 1 = 3.50 d = 5 n = 30 A n = A 1 + (n-1) d A 30 = 3.50 + (30-1) (5) A 30 = 3.50 + (29) (5) A 30 = 3.50 + 145 A 30 = 148.50

12. The terms between any two nonconsecutive terms of an arithmetic sequence. Arithmetic Means

13. Insert 4 arithmetic means between 5 and 25. Example Let A 1 = 5 A 6 = 25 d=? 5, A 2 , A 3 , A 4 , A 5 , 25

14. Solution: A n = A 1 + (n-1)d 25 = 5 + (6-1)d 25 = 5 + (5)d 25 = 5 + 5d 25-5 = 5d 20 = 5d 5 5 d = 4 5 + 4 = 9 9 + 4 = 13 13 + 4 = 17 17 + 4 = 21 5, 9 , 13 , 17 , 21 , 25