Chapter 12 Sequence and Series

Arithmetic

100

Write a rule for the nth term of the arithmetic sequence: -8, -5, -2, 1, 4,  . . .

a_n = 3n - 11

200

Write a rule for the nth term of the arithmetic sequence: 4, 17, 30, 43, 56, . . . 

a_n = 13n - 9

300

Write a rule for the arithmemtic sequence where a₈ = 23 and d = 7

a_n = 7n - 33

400

Write a rule for the arithmetic series where a₁₂ = -14 and d = - 4.

a_n = -4n + 34

500

Write a rule for the arithmetic sequence where a₆ = 18 and a₁₈ = 66. 

a_n = 4n - 6

Geometric

100

Write a rule for the nth term of the geometric sequence: 1, 3, 9, 27, 81, 243, . . . 

a_n = 1(3)^n-1

200

Write a rule for the nth term of the geometric sequence: 256, 64, 16, 4, 1, . . . 

a_n = 256(1/4)^n-1

300

Write a rule for the geometric sequence where a₄ = 24 and r = 2/3

a_n = 81(2/3)^n-1

400

Determine a₁₂ for the following geometric sequence: 8, -24, 72, -216, 648, . . . 

a₁₂ = -1,417,176

500

Write a rule for the nth term of the geometric sequence where a₃ = 54 and a₆ = 16           

a_n = 121.5(2/3)^n-1

Quadratic/Squares/Cubes

100

Find a₂₀ for the following quadratic sequence that has the rule: a_n = (3n - 1)(2n + 1)

a₂₀ = 2,419

200

Write a rule for the nth term of the sequence: 2, 5, 10, 17, 26, 37, . . . 

a_n = n² + 1

300

Write a rule for the nth term of the quadratic sequence: 0, 1, 3, 6, 10, 15

a_n = [(n-1) n ] / 2

400

Write a rule for the nth term of the sequence: -2, 5, 24, 61, 122, . . .

a_n = n³ - 3

500

Write a rule for the nth term of the quadratic sequence: -1, 0, 9, 26, 51, 84

a_n = (n - 2)(4n - 3)

Random

100

Identify the first 5 terms of the sequence that has the given rule: a_n = 2n - 1

1, 3, 5, 7, 9

200

Write a recursive rule for the following sequence: 7, 1, -5, -11, -17, . . . 

a_n = (a_n-1) - 6

300

Write a recursive rule for the following sequence: 64, 32, 16, 8, 4, 2, . . . 

a_n = (a_n-1) x 1/2

400

How many handshakes would occur in a room full of 20 people?

190

500

How far would a tire swing travel before coming to a rest, if it released with a first initial swing of 50ft and each successive swing travels 60% of the previous swing. 

125ft

Series

100

Find S₁₀ of the following series: 1 + 4 + 7 + 10 + 13 + . . . 

145

200

Find S₁₅ for the following series: 2 + 4 + 8 + 16 + 32 + . . . 

65534

300

Find the sum of the infinite geometric series: 12 + 4 + 4/3 + 4/9 + . . . 

18

400

What is the sum of the first 30 even numbers: 2 + 4 + 6 + . . . 

930

500

What is the sum of the first 20 odd numbers: 1 + 3 + 5 + . . . 

400