Math Algebra 12.2 Practice Worksheet Key

University:
Carleton College
Course:
MATH 111 | lntroduction to Calculus
Academic year:

2022
Views:

117

Pages:

3
Author:

McGowanfgu

Algebra 2 CP Practice Worksheet Name: (Key) Assignment 12.2-12.3 Tell whether the following sequences are arithmetic or geometric, find the next term in the sequence, and then find d or r. 1. 3, 12, 48, 192, 768, ... Geometric; 3072 r = 4 2. -3, -1, 1, 3, 5, ... Arithmetic; 7 d = 2 3. 100, 50, 25, 25/2, 25/4, ... Geometric; 25/8 r = 1/2 4. 8, 4, 0, -4, -8, -12, ... Arithmetic; -16 d = -4 Determine whether the sequence is arithmetic or geometric, write a rule for the nth term of the sequence, and then find a₈. 5. -25, -29, -33, -37, ... d = -4 an = -25 + (n-1)(-4) = -25 - 4n + 4 an = -21 - 4n a₈ = -53 6. 6, 2, 2/3, 2/9, 2/27, ... r = 1/3 an = 6(1/3)^(n-1) a₈ = 2/2187 7. 2, 8, 32, 128, ... r = 4 an = 2(4)^(n-1) a₈ = 32768 8. 4, 8, 12, 16, ... d = 4 an = 4 + (n-1)4 = 4 + 4n - 4 an = 4n a₈ = 32 9. 7, 10, 13, 16, ... d = 3 an = 7 + (n-1)3 = 7 + 3n - 3 an = 4 + 3n a₈ = 28 10. 3, 12, 48, 192, ... r = 4 an = 3(4)^(n-1) a₈ = 49152 Write a rule for the nth term of the arithmetic or geometric sequence. Then find a₂₀. 11. a₅ = 15 and d = 5 15 = a₁ + 4(5) a₁ = -5 an = -5 + (n-1)5 = -5 + 5n - 5 an = -10 + 5n a₂₀ = -10 + 5(20) = 90 12. a₂ = 3, r = 2 an = 3(2)^(n-1) a₂₀ = 3(2)^19 = 1572864 13. a₁₀ = 150 and d = -5 150 = a₁ + 9(-5) a₁ = 195 an = 195 + (n-1)(-5) = 195 - 5n + 5 an = 200 - 5n a₂₀ = 200 - 5(20) = 100 14. a₂ = 2, r = 1/2, a₁ = 4 an = 4(1/2)^(n-1) a₂₀ = 4(1/2)^19 = 1/2^17 Write a rule for the nth term of the arithmetic sequence given two terms. 15. a₂₀ = 240, a₁₅ = 170 240 = a₁ + 19d 170 = a₁ + 14d ------------------- 70 = 5d d = 14 a₁ = 240 - 19(14) = -26 an = -26 + (n-1)14 = -26 + 14n - 14 an = -40 + 14n a₂₀ = -40 + 14(20) = 240 16. a₁₆ = 6, a₂₀ = 7 6 = a₁ + 15d 7 = a₁ + 19d ------------------- -1 = -4d d = 1/4 a₁ = 6 - 15(1/4) = 9/4 an = 9/4 + (n-1)(1/4) = 9/4 + 1/4n - 1/4 an = 2 + 1/4n Write a rule for the nth term of the geometric sequence given two terms. 17. a₂ = 36, a₄ = 576 36 = a₁(r)^1 576 = a₁(r)^3 ------------------- r² = 16 r = ±4 a₁ = ±9 an = 9(4)^(n-1) or an = -9(-4)^(n-1) 18. a₂ = 4, a₅ = 256/27 4 = a₁(r)^1 256/27 = a₁(r)^4 ------------------- 4 = 64/27 r = 4/3 a₁ = 3 an = 3(4/3)^(n-1)

Math Algebra 12.2 Practice Worksheet Key

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