University:
North Central College
Course:
MATH 151 | Calculus I
Academic year:

2019
Views:

184

Pages:

6
Author:

larbiwxcvbn

8.1-8.3 8.5 Review Name: Hour: State whether each type of sequence is arithmetic, geometric, or neither, and find the nth term. Assume n begins with 1. 1 1. 1. 17, 13, 9, 5... Arithmetic d = -4 An = 17 - 4(n - 1) An = -4n + 21 2. 1/3, 4/5, 9/7, 16/9... neither numerator: list of perfect squares denominator: arithmetic An = n² / (2n + 1) 3. -1, 1/4, -1/16, 1/64... Geometric A₁ = -1, r = -1/4 An = -1(-1/4)^(n-1) 4. 3, 18, 108, 648... a₁ = 3, r = 6, geometric An = 3(6)^(n-1) 5. 1/2, 1/9, 1/26, 1/65, 1/126... neither numerator: 1 denominator: 1 more than the list of perfect cubes An = 1 / (n³ + 1) 6. 2, 4, 2, 4, 2... neither, alternating An = 3 + (-1)^n 7. 28, 24, 20, 16, 12... Arithmetic d = -4 An = 28 - 4(n - 1) An = -4n + 32 8. 1/3, -2/3, 4/3, -8/3... Geometric A₁ = 1/3, r = -2 An = 1/3(-2)^(n-1) 9. 9, 6, 4... Geometric a₁ = 9, r = 2/3 An = 9(2/3)^(n-1) 10. n² + 2 / 4n + 1 neither numerator: arithmetic denominator: arithmetic A₁ = 3 d = 4 In #11 and #12, write the first five terms of the sequence. Assume n begins with 1. 11. An = (1 + (-1)^n) / 2n A₁ = 0 A₂ = 1/2 A₃ = 0 A₄ = 1/4 A₅ = 0 12. An = √(n + 1) / n A₁ = √2 A₂ = √3/2 A₃ = √4/3 = 2/3 A₄ = √5/4 A₅ = √6/5 13. In a geometric sequence, a₄ = -12 and a₉ = 96. Find a₁₄. -12 = a₁r³ 96 = a₁r⁸ 96/-12 = r⁵ -8 = r⁵ r = -2 -12 = a₁(-8)³ a₁ = 3/2 An = 3/2(-2)^(n-1) A₁₄ = 3/2(-2)¹³ = -12,288 14. In a geometric sequence, a₄ = 125 and a₁₀ = 125/64. Find a₁₅. 125/64 = a₄r⁶ 125/64 = 125r⁶ 1/64 = r⁶ r = ±1/2 125 = a₁(±1/2)³ a₁ = ±1000 An = ±1000(±1/2)^(n-1) A₁₅ = ±1000(1/2)¹⁴ = 125/2048 15. In an arithmetic sequence, a₃ = 11 and a₈ = 39. Find a₁₇. 39 = a₁ + d(8-1) → 39 = a₁ + 7d 11 = a₁ + d(3-1) → 11 = a₁ + 2d 28 = 5d d = 4 11 = a₁ + 2(4) a₁ = 3 An = 3 + 4(n-1) A₁₇ = 3 + 4(17-1) A₁₇ = 102 16. In an arithmetic sequence, a₃ = 13 and a₁₀ = 41. Find a₄₃. 41 = a₁ + d(10-1) → 41 = a₁ + 9d 13 = a₁ + d(3-1) → 13 = a₁ + 2d 28 = 7d d = 4 13 = a₁ + 2(4) a₁ = 5 An = 5 + 4(n-1) A₄₃ = 5 + 4(43-1) A₄₃ = 173 Give a recursive definition for the following sequences. Don't forget to state the first term! The formula means NOTHING without 1 1. it! 17. 2, -4, 8, -16,... a₁ = 2 An+1 = -2An 18. 3, 6, 12, 24,... a₁ = 3 An = 2An-1 19. -256, 64, -16, 4,... a₁ = -256 An+1 = -1/4An 20. 51, 43, 35, 27,... a₁ = 51 An = An-1 - 8 21. Which term of the arithmetic sequence -1, 4, 9, ..., is 374? 374 = -1 + 5(n-1) 375 = 5(n-1) 75 = n-1 n = 76