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- 8. REVIEW GAMES LESSON ACTIVITY GENERALIZATION QUIZ AGREEMENT Raise thumbs up if the given sequence is arithmetic and thumbs down if it is not arithmetic.
- 15. REVIEW LESSON GAMES ACTIVITY GENERALIZATION QUIZ AGREEMENT An arithmetic sequence is a sequence in which each term after the first is found by adding a constant, called common difference d, to the previous term.
- 16. REVIEW LESSON GAMES ACTIVITY GENERALIZATION QUIZ AGREEMENT Consider this sequence: 4, 6, 8, 10, . . . a1 a2 a3 a4 d = common difference d d d d = 6-4 = 8-6 = 10-8 = 2
- 17. REVIEW LESSON GAMES ACTIVITY GENERALIZATION QUIZ AGREEMENT an = a1 +(n-1)d ARITHMETIC SEQUENCE FORMULA Where: an = nth term a1 = first term n = the number of terms d = common difference
- 18. REVIEW LESSON GAMES ACTIVITY GENERALIZATION QUIZ AGREEMENT Arithmetic Sequence: 4, 6, 8, 10, . . . a1 a2 a3 a4 d= 2 a1 4 a a a 6 8 10 4 +2 4+2+ 4+2 2 +2+2 4 (2) (2) (2) (3) (2) 4 4 2 (1) 3 4 a1 +(n-1)d an + + +
- 19. REVIEW LESSON GAMES ACTIVITY GENERALIZATION QUIZ AGREEMENT an = a1 +(n-1)d ARITHMETIC SEQUENCE FORMULA Where: an = nth term a1 = first term n = the number of terms d = common difference
- 20. REVIEW LESSON GAMES ACTIVITY GENERALIZATION QUIZ AGREEMENT Examples: 1. Find the 21st term of the arithmetic sequence: 4, 7, 10, 13, โฆ Solution an = a1 +(n-1)d a1= 4 d= 3 n= 21 a21 = 64 a21 = 4 + (21-1)3 a21 = 4 + (20)3 a21 = 4 + 60 Thus, the 21st term is 64.
- 21. REVIEW LESSON GAMES ACTIVITY GENERALIZATION QUIZ AGREEMENT Examples: 2. Find the 14th term of the arithmetic sequence 5, 7, 9, 11, โฆ Solution: an = a1 +(n-1)d a1= 5 d= 2 n= 14 a a14 = 5 + a14 = 5 + a14 = 31 Thus, the 14th term is 31. Given: 2 = 5 +( -1) (13)2 26 14 14
- 22. REVIEW LESSON GAMES ACTIVITY GENERALIZATION QUIZ AGREEMENT Examples: 3. Given two terms in the arithmetic sequence, a5= - 8 and a25 =72 a5= -8 Given: a) Write a rule that can find any term in the sequence. b) Find the 100th term (a100) a25 = 72 Find:
- 23. REVIEW LESSON GAMES ACTIVITY GENERALIZATION QUIZ AGREEMENT Solution: ๐๐ = ๐๐ + ๐ โ ๐ ๐ ๐๐ = ๐๐ + ๐ โ ๐ ๐ -8= ๐๐ + 5 โ 1 ๐ -8= ๐๐ + 4๐ Equation 1 72= ๐๐ + 25 โ 1 ๐ 72= ๐๐ + 24๐ Equation 2 -8= ๐๐ + 4๐ Equation 1 72= ๐๐ + 24๐ Equation 2 USE ELIMATION METHOD -80= โ20๐ 4=d
- 24. REVIEW LESSON GAMES ACTIVITY GENERALIZATION QUIZ AGREEMENT ๐๐ = ๐๐ + ๐ โ ๐ ๐ ๐๐ = ๐๐ + ๐ โ ๐ ๐ -8= ๐๐ + 5 โ 1 ๐ -8= ๐๐ + 4๐ Equation 1 72= ๐๐ + 25 โ 1 ๐ 72= ๐๐ + 24๐ Equation 2 Solution: 4=d -8= ๐๐ + 4๐ Substitute the value of d, -8= ๐๐ + 4(4) -8= ๐๐ + 16 -8= ๐๐ + 16-16 -16 -24=๐๐ ๐๐ = ๐๐ + ๐ โ ๐ ๐ -24=๐๐ ๐๐ = โ๐๐ + ๐ โ ๐ ๐
- 25. REVIEW LESSON GAMES ACTIVITY GENERALIZATION QUIZ AGREEMENT Solution: ๐๐ = โ๐๐ + ๐ โ ๐ ๐ b) Find the 100th term (a100) ๐๐๐๐ = -24 + 100 โ 1 4 ๐๐๐๐ = -24 + 99 4 ๐๐๐๐ = -24 + 396 ๐๐๐๐ = 372
- 26. REVIEW LESSON ACTIVITY GAMES GENERALIZATION QUIZ AGREEMENT 1. Find the 16th term of the sequence 1, 5, 9, 13, โฆ 2. Find the 11th term of the arithmetic sequence 3, 4, 5,โฆ 3. Find the 20th term of the arithmetic sequence 17, 13, 9,โฆ 4. If a1 = 5 and a7= 17, find the common difference. 5. In the sequence 50, 45, 40, 35, โฆ , which term is 5? Solve the following sequence
- 27. REVIEW LESSON ACTIVITY GAMES GENERALIZATION QUIZ AGREEMENT 1. Find the 16th term of the sequence 1, 5, 9, 13, โฆ Solution: an = a1 +(n-1)d a1= 1 d= 4 n= 16 Given: a16 = 1 +(16-1)4 a16 = 1 +(15)4 a16 = 1 +60 a16 = 61 Thus, the 16th term is 61.
- 28. REVIEW LESSON ACTIVITY GAMES GENERALIZATION QUIZ AGREEMENT 2. Find the 11th term of the arithmetic sequence 3, 4, 5,โฆ Solution: an = a1 +(n-1)d a1= 3 d= 1 n= 11 Given: a13 = 3 +(11-1)1 a13 = 3 +(10)1 a13 = 3 +10 a13 = 13 Thus, the 16th term is 13.
- 29. REVIEW LESSON ACTIVITY GAMES GENERALIZATION QUIZ AGREEMENT 3. Find the 20th term of the arithmetic sequence 17, 13, 9,โฆ Solution: an = a1 +(n-1)d a1= 17 d= -4 n= 20 Given: a20 = 17 +(20-1)-4 a20 = 17 +(19)-4 a20 = 17 +(-76) a20 = -59 Thus, the 20th term is -59.
- 30. REVIEW LESSON ACTIVITY GAMES GENERALIZATION QUIZ AGREEMENT 4. If a1 = 5 and a7= 17, find the common difference. Solution: 17 = 5 +(7-1)d a1= 5 d= ? n= 7 Given: a7= 17 17 = 5 +(6)d 17 -5= 6d 12= 6d 2= d an = a1 +(n-1)d
- 31. REVIEW LESSON ACTIVITY GAMES GENERALIZATION QUIZ AGREEMENT 5. In the sequence 50, 45, 40, 35, โฆ , which term is 5? Solution: 5 = 50 +(n-1)-5 a1= 50 d= -5 n= ? Given: an = a1 +(n-1)d 5 = 50 + (-5n+5) an = 5 5 = 50 -5n + 5 5 = 50 + 5 -5n 5 = 55 - 5n 5 - 55 = - 5n -50= - 5n 10= n Thus, 5 is the 10th term.
- 32. REVIEW LESSON ACTIVITY GAMES GENERALIZATION QUIZ AGREEMENT Practical applications of concepts and skills in daily living After one second, a rocket is 30 ft above the ground. After another second, it is 85 feet above the ground. Then after another second, it is already 140 feet above the ground. If it continues to rise at this rate, how many feet above the ground will the rocket be after 16 seconds?
- 33. REVIEW LESSON ACTIVITY GAMES GENERALIZATION QUIZ AGREEMENT a. From the problem we let the given a1= 30 a2= 85 a3= 140 b. Find first d by substitution the given value of a1 ๐๐๐ a2 in the formula then simplify an = a1 +(n-1)d 85 = 30 +(2-1)d 85-30 = d 55 = d
- 34. REVIEW LESSON ACTIVITY GAMES GENERALIZATION QUIZ AGREEMENT to find a16 the unknown in the problem substitute the obtained value of d and the given value of a1 in the formula then simplify an = a1 +(n-1)d Thus, the rocket will b 855 ft above the ground after 16 seconds. a16 = 30 +(16-1)55 a16 = 30 +(15)55 a16 = 30 +825 a16 = 855
- 35. REVIEW LESSON ACTIVITY GAMES GENERALIZATION QUIZ AGREEMENT 1. State the general formula of finding the nth term of an arithmetic sequence What I have Learned? an = a1 +(n-1)d Answer the following questions.
- 36. REVIEW LESSON ACTIVITY GAMES GENERALIZATION QUIZ AGREEMENT 2. Given an arithmetic sequence, how do we find the common difference? A common difference is the difference between consecutive numbers in an arithmetic sequence.
- 37. REVIEW LESSON ACTIVITY GAMES GENERALIZATION QUIZ AGREEMENT 3. Given two different nth terms of an arithmetic sequence, how do we find for the common difference? We can subtract the terms and divide by the difference in term number to determine the common difference.
- 39. REVIEW LESSON ACTIVITY GAMES GENERALIZATION QUIZ AGREEMENT 1. Find the 22nd term of the following sequence: 5, 8, 11, .. a. 60 b. 63 c. 66 d. 68 d. correct
- 40. REVIEW LESSON ACTIVITY GAMES GENERALIZATION QUIZ AGREEMENT 2. Find the 32nd term of this sequence. 34, 37, 40, 43, ... a. 32 b. 127 c. 64 d. 356 b. 127 correct!
- 41. REVIEW LESSON ACTIVITY GAMES GENERALIZATION QUIZ AGREEMENT 3. Find the 25th term of the sequence if a1 = 5 and d = 0.5 a. 18 c. 17 d. 13 b. 14 c. 17 correct!
- 42. REVIEW LESSON ACTIVITY GAMES GENERALIZATION QUIZ AGREEMENT 4. Find the first term of the given sequence: a18=68 and d=1 a. 4 c. 20 d. 9 b. 6 a. 4 correct!
- 43. REVIEW LESSON ACTIVITY GAMES GENERALIZATION QUIZ AGREEMENT 5. Find the 35th term in the arithmetic sequence 3, 9, 15, 21, โฆ a. 200 b. 207 correct! c. 165 d. 205 b. 207
- 44. REVIEW LESSON ACTIVITY GAMES GENERALIZATION QUIZ . AGREEMENT Try to derive the formula for geometric sequence References: Self Learning Module in Math 10 Learning Guide Math 10