4. quadratic sequence.pptx gdgdgdgdgdgdgd

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1. Mathematics 10 SEQUENCE Day 4 Mr. Rosilito E. Gonzales August 8, 2024

2. PRAYER Dear Lord, we thank You a hundredfold for the love and care that You have given us. May we in return to You, Your good works, multiply it with love and respect. Add more faith. Subtract the unworldly behavior and evil works but divide Your given talents to others. And to sum it all may we be united in Your family. In this we pray, Amen.

3. Answer to the assignment a n = 8n - 2 a n = -4n + 13 a n = 7n - 2 a n = -6n + 26

4. OBJECTIVES: Show mastery of the different concept taken, Forming the general rule given the quadratic sequence. 4

5. Find the GENERAL TERM of the following sequence. 1. 4, 12, 20, 28, … 2. 10, 5, 0, -5, … 3. -2, -10, -18, -26, … REVIEW:      

6. Observe the sequence below: 6, 13, 24, 39, 58, … Is the sequence a Linear Sequence? Why or Why not?

7. Quadratic sequence

8. Quadratic sequence A QUADRATIC SEQUENCE is a sequence of numbers in which the second differences between each consecutive term is constant, called a common second difference. The General Form is:  

9. Example 1. Find the general term of the given sequence. 6, 13, 24, 39, 58, … 9 Find the first and second differences of the given sequ ence

10. 10   3) a+b+c=a 1   2+1+c=6   3+c=6   c=6-3   c=3  1) 2a=second difference   2a=4   a=2   2) 3a+b=first term in the first differences   3(2)+ba=7   6+b=7   b=7-6   b=1

11. Substitute the resulting value of a, b and c in the general for: a n =an 2 +bn+c a = 2 b = 1 c = 3 a n =2n 2 +n+3 11

12. Try this: Find the general term of the given sequence. 0, 1, 4, 9, 16, … 12 a n =n 2 - 2n+1

13. EXERCISES: Find the GENERAL TERM of the following Quadratic Sequence: 1. 7, 13, 23, 37,… 2. 6, 11, 18, 27,… 3. -1, 1, 7, 17,…      

14. Assignment: find the general term of the following sequence. 1, 18, 45, 82, 129 3, 13, 27, 45, 67 -1, 4, 19, 44, 79 14

15. Thank you