Find the first three terms of the sequence given by a(n) = (3n^2 + n – 2)/(2n^2 + 1)
What is 2/3, 12/9, 28/19
100
Find the first five terms of the geometric sequence where a(1)=3 and r=4
What is 3, 12, 48, 192, 768
100
A parabola has vertex (4,2) and focus (2,2). Find the standard form of the equation.
What is (y-2)^2 = -8(x-4)
200
Simplify: (2x - 3y)(3x + 2y)
What is 6x^2 +-5xy - 6y^2
200
Use the properties of logs to expand log 4(x^2)y
What is Log 4 + 2log x + log y
200
Find the first five terms of the sequence where a(1) = 4 and a(k+1) = a(k) + 6
What is 4, 10, 16, 22, 28
200
Find the 32nd term of the sequence 3, 6, 12, 24, . . .
What is 6,442,450,944
200
A hyperbola has vertices (0,±2) and foci (0,±5). Find the standard form of the equation of this hyperbola.
What is (y^2)/4 - (x^2)/21 = 1
300
Factory: x^2 - 36
What is (x + 6)(x - 6)
300
Write the expression as a single quantity: log_4 (10) - log_4 (t) + log_4 (z)
What is log_4 (10z/t)
300
Evaluate: 5
Σ (k+5) / k
K=1
What is 16 5/12
300
Simplify: (3n+2)! / (3n)!
Leave your answer in factored form.
What is (3n+2)(3n+1)
300
An ellipse has major vertices (4,0) and (4,4); the minor axis has length 2. Find the standard form of the equation of this ellipse.
What is (x-4)^2/1 + (y-2)^2/4 = 1
400
Solve: 2x^2 - 5x - 3 = 0
What is -1/2 and 3
400
Solve for x:
4^(4x) = 2000
(Round your answer to 4 decimal places)
What is 1.3707
400
An auditorium has 20 row seats. There are 12 seats in the first row, 14 seats in the second row, 16 seats in the third row, and so on. How many seats are in the 15th row?
What is 40
400
Evaluate: 15
Σ 3^(n-1)
n=1
What is 7,174,453
400
Find the vertex of the parabola with equation y^2 + 4y + 10x + 24 = 0.
What is (-2,-2)
500
Simplify: (x^2 + 2x-8)/(x^2- 16)
What is (x - 2)/(x - 4)
500
Solve for x:
4log (x-4) = 16
What is 10004
500
Evaluate: 64
Σ (n + 4)
n=0
What is 2,340
500
Evaluate: ∞
Σ (1/3)^n
n=0
What is 3/2
500
Find the center of the ellipse with equation 9x^2 + 4y^2 - 54x + 32y + 109 = 0