Arithmetic sequence grade 10 mathematics.pptx

arithmetic sequence

1. Arithmetic sequence MARK O. AGUSTIN, LPT

2. LEARNING COMPETENCIES Find the common difference and the nth term of an arithmetic sequence. Solve problems involving arithmetic sequence LEARNING objectives Illustrate an arithmetic sequence Determine the nth terms of an arithmetic sequence. Solve problems involving sequences.

3. Essential question How do you compute for the common difference of an arithmetic sequence? How do you find the nth term of an arithmetic sequence?

4. Arithmetic sequence Also known as arithmetic progression A sequence where each term after the first is obtained by adding a constant (called the common difference ) to the preceding term. Ex. 4, 8, 12, 16 -5, -2, 1, 4

5. term Each value in a sequence Ex. 4, 8, 12, 16 the 1 st term is 4, 2 nd term is 8, 3 rd term is 12, 4 th term is 16 and so on.

6. General term of a sequence Where: = nth term = 1 st term =number of terms = common difference  

7. Illustrative example Find the 20 th term in the sequence 6, 13, 20, 27, … Solution: Find the common difference d=  

8. Illustrative example Find the 20 th term in the sequence 6, 13, 20, 27, … Therefore, the 20 th term is 139 .  

9. Illustrative example 2. List all given  

10. Illustrative example Find the 30 th term in the sequence if the 5 th term is -10 and the common difference is 6. Given: 5 th term= -10 d= 6

11. Illustrative example Find the 30 th term in the sequence if the 5 th term is -10 and the common difference is 6. Solution: First find  

12. Illustrative example Find the 30 th term in the sequence if the 5 th term is -10 and the common difference is 6. Solution: find Therefore, the 30 th term is 140 .  

13. Illustrative example In the arithmetic sequence, the 4 th term is 30 and the 10 th term is 66. find the 8 th term.

14. Illustrative example Given the arithmetic sequence , find the 10 th term  

15. Illustrative example In an arithmetic sequence, the 5 th term is 24 and the 11 th term is 60. what is the common difference.

16. Illustrative example The 4 th term of an arithmetic sequence is -1 and the 6 th term is 9. write the first eight terms of the sequence.

17. Illustrative example Reymund decided to join a gym’s weight loss program. One week after joining, he starts losing a constant amount of weight. Five weeks after joining the gym, he weighs 165 kg. ten weeks after, he weighs 150 kg. assuming that the patterns continues, find his weight before joining the gym and the amount of weight he lost per week.