SEQUENCES & PATTERNS
Given the sequence 7, 11, 15, 19, ... , which function defines the nth term of this sequence?
(1) a_n = 4n + 3
(2) a_n = 4n + 7
(3) a_n = 3n + 4
(4) a_n = 7n + 4
(1) a_n = 4n + 3
Which explicit formula represents the geometric sequence 3, 6, 12, 24, ... ?
(1) a_n = 3(2)^n
(2) a_n = 3(2)^{n-1}
(3) a_n = 2(3)^{n-1}
(4) a_n = 3 + 3(n-1)
(2) a_n = 3(2)^{n-1}
If f(x) = 2x^2 - 3x + 4 , what is the value of f(-3) ?
(1) -23
(2) -5
(3) 13
(4) 31
(4) 31
A computer system originally purchased for 1,200 depreciates in value at a rate of 12% per year. Which function models the value, V(t) , of the computer after t years?
(1) V(t) = 1200(0.12)^t
(2) V(t) = 1200(0.88)^t
(3) V(t) = 1200 - 12t
(4) V(t) = 1200(1.12)^t
(2) V(t) = 1200(0.88)^t
The first four terms of a sequence are 12, 6, 3, 1.5,... . Which statement best describes this sequence?
(1) It is arithmetic with a common difference of -6.
(2) It is arithmetic with a common difference of 0.5.
(3) It is geometric with a common ratio of 2.
(4) It is geometric with a common ratio of 0.5.
(4) Geometric with a common ratio of 0.5
An arithmetic sequence has an explicit formula of f(n) = 2n + 5. Which recursive formula represents the exact same sequence?
(1) f(1) = 5, \quad f(n) = f(n-1) + 2
(2) f(1) = 7, \quad f(n) = f(n-1) + 2
(3) f(1) = 5, \quad f(n) = 2f(n-1)
(4) f(1) = 7, \quad f(n) = 2f(n-1)
(2) f(1) = 7, \quad f(n) = f(n-1) + 2
Which coordinate pair lies on the graph of g(x) = \abs {2x - 5} + 1 ?
(1) (1, 4)
(2) (2, 5)
(3) (-1, 6)
(4) (3, 10)
(1) (1, 4)
A school store sells t-shirts for $15 each. The school paid a one-time setup fee of $50. The profit function is P(n) = 15n - 50 , where n represents the number of t-shirts sold up to a maximum of 200 t-shirts. Which domain is most appropriate for this function?
(1) All real numbers
(2) 0 \le n \le 200 , where n is a continuous real number
(3) Whole numbers from 0 to 200
(4) All integers
(3) Whole numbers from 0 to 200
A sequence is recursively defined by a_1 = 5 and a_n = 3a_{n-1} - 2 for n > 1 .
Determine the value of a_4 . Show all work.
a_4 = 109
Given the sequence 18, 14, 10, 6,... :
Write an explicit formula, a_n , for the n\text{th} term of the sequence.
Use your formula to find the value of a_{20} .
Part 1: a_n = 18 - 4(n - 1) or a_n = -4n + 22
Part 2: a_{20} = -4(20) + 22 = -58 .
Given the function h(x) = \sqrt{x + 9} - 2 :
Algebraically determine whether the point
(16, 3) lies on the graph of h(x). Justify your answer.
YES, the point (16, 3) lies on the graph.
A car rental company charges a flat fee of $45 plus $0.20 per mile driven.Write a linear function, C(m) , that represents the total cost of renting a car and driving it m miles.
C(m) = 0.20m + 45 (or C(m) = 45 + 0.20m )