Mathematics 10 Quarter I Arithmetic Sequence

After going through this lesson, students are expected to:
1. define an arithmetic sequence,
2. illustrate an arithmetic sequence, and
3. find the nth term of an arithmetic sequence.


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1. ARITHMETIC SEQUENCE REGIE R. NAUNGAYAN Teacher III, DepEd Banayoyo NHS

2. After going through this module, you are expected to: 1. define an arithmetic sequence , 2. illustrate an arithmetic sequence and 3. finding the nth term of an arithmetic sequence .

3. TABLE OF CONTENTS Illustrating Arithmetic Sequence 01 02 Finding the nth Term of an Arithmetic Sequence

4. MIND EXERCISE Determine the next three terms of the sequences. 1. 5, 12, 19, 26, … 2. 33, 38, 43, 48, … 3. -14, -10, -6, -2, … 33, 40, 47 53, 58, 63 2, 6, 10

5. How did you determine the terms in the sequence?

6. Arithmetic Sequence A sequence whose consecutive terms have a common difference is an arithmetic sequence . The sequence a 1 , a 2 , a 3 , …, a n is arithmetic if there is a number d such that: a 2 – a 1 = d , a 3 – a 2 = d , a 4 – a 3 = d . d is called the common difference .

7. 2, 5, 8, 11, 14, … Is this an arithmetic sequence? 3 3 3 3 d = 3 YES

8. -1, -4, -7, -11, -14, … What about this? -3 -3 -4 -3 There is no common difference. NOT ARITHMETIC

9. ACTIVITY 1: Arithmetic or not? Which of the following is an arithmetic sequence? If the sequence is arithmetic, determine the common difference , but write NA is not an arithmetic sequence. 3, 0, -3, -6, -8, … -15, -10, -5, 0, 5, … 2, 13, 15, 28, 43, … 17, 23, 29, 35, 41, … , 1, , 2, , …   NA d = 5 NA d = 6 d = 1/2

10. ACTIVITY 2: What’s the difference? 27, 21, 15, 9, 3, … 6, 10, 14, 18, 22 6, 4, 2, 0, -2, … -20, -13, -6, 1, 8, … -1, 4, 9, 14, 19, … d = -6 d = 4 d = -2 d = 7 d = 5 Determine the common difference of the following arithmetic sequences:

11. ACTIVITY 3: C o mplete me! The following sequences are arithmetic. Complete them by supplying the correct term/s. 5, 9, 13, __, 21, … -14, -7, __, 7, 14, … __, 10, 22, 34, 46, … 50, __, 28, 17, 6, … 6.2, 6.7, 7.2, 7.7, __, … 17 -2 39 8.2

12. FINDING THE NTH TERM OF AN ARITHMETIC SEQUENCE 02

13. What is the 6 th term of the sequence 4 , 11 , 18 , 25 , …? Answer: 39

14. What is the 75 th term of the sequence 4 , 11 , 18 , 25 , …? HOW???

15. Formula a n = a 1 + (n-1)d a n = the nth term a 1 = first term n = number of terms/the position of the term being solved d = common difference

16. a n = a 1 + (n-1)d a n = a 75 a 1 = 4 n = 75 d = 7 What is the 75 th term of the sequence 4 , 11 , 18 , 25 , …? a 75 = 4 + (75 – 1)(7) a 75 = 4 + (74)(7) a 75 = 4 + 518 a 75 = 522

17. a n = a 9 a 1 = -1 n = 9 d = 6 What is the 9 th term of the sequence -1 , 5 , 11 , 17 , 23 , …? a n = a 1 + (n – 1)d a 9 = -1 + (9 – 1)(6) a 9 = -1 + (8)(6) a 9 = -1 + 48 a 9 = 47

18. a n = a 11 a 1 = -4 n = 11 d = 3 What is the 11 th term of the sequence whose first term is -4 and common difference of 3 ? a n = a 1 + (n – 1)d a 11 = -4 + (11 – 1)(3) a 11 = -4 + (10)(3) a 11 = -4 + 30 a 11 = 26

19. a n = a 7 a 1 = 23 n = 7 d = -5 If a 1 = 23 , and d = -5 , what is a 7 ? a n = a 1 + (n – 1)d a 7 = 23 + (7 – 1)(-5) a 7 = 23+ (6)(-5) a 7 = 23 – 30 a 7 = - 7

20. Challenge Question If a 13 = 112 , and d = -8 , what is the first term?

21. a n = 112 a 1 = ? n = 13 d = -8 If a 13 = 112 , and d = -8 , what is the first term? a 1 = a n – (n – 1)d a 1 = 112 – (13 – 1)(-8) a 1 = 112 - (12)(-8) a 1 = 112 – (-96) a 1 = 112 + 96 a 1 = 208 a n = a 1 + (n – 1)d

22. ACTIVITY 1: What’s my nth? Determine the indicated term of each arithmetic sequence. 2, 8, 14, 20, 26, …, a 21 -12, -7, -2, 3, 8, …, a 14 18, 15, 12, 9, 6, …, a 15 1, -4, -9, -14, -19, …, a 9 1.2, 1.7, 2.2, 2.7, …, a 10 122 53 60 -39 5.7

23. ACTIVITY 2: Choose the right one! From the two choices, select the value that corresponds to the indicated term of the arithmetic sequence. a 1 = -2, d = 4, a 8 = ___ a 1 = 1, d = 9, a 12 = ___ a 1 = 25, d = -3, a 15 = ___ a 1 = 2.5, d = 2, a 20 = ___ a 10 = -10, d = -2, a 1 = ___ 26 100 17 25 8 28 109 -17 40.5 -12

24. Let’s SUMMARIZE W hat is an arithmetic sequence? H ow do we know if a sequence is arithmetic? H ow do we determine the nth term of an arithmetic sequence?

25. THANK YOU!