Sequences & Series Questions and Answers

A coordinate plane is formed by two intersecting number lines. The horizontal line is called the x-axis. The vertical line is called the y-axis. This two-axis system is called the coordinate system The coordinates of a point are Quadrant II represented by the ordered pair (x, y). This shows the distance the point is from the origin (0, 0), in the domain (the set of x coordinates) and the range (the set of y coordinates). A set of ordered pairs is called a relation. In the graph at right, Point A is located at (4, 2). Point B is located When two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. The coordinates of Point C differ from the coordinates of Point B by only the sign of the x-coordinate. So Point C, located at (5, -3), is a reflection of Point B across the y-axis. Write the ordered pair for each lettered point on the grid.

A sequence is defined recursively by the given formulas. Find the first five terms of the sequence. an = 2(an -1 + 3) and a₁ = 4 a1 = a2 = a3 = a4 = a5 =

Traffic control. The graph below shows how the number of traffic signals in a city changed over a 10-year period. Find the average rate of change in the number of traffic signals.

Which of the following ordered pairs is within the solution set to the following system of inequalities? x²-y≤ 3x-2 (1/2)x+1<-y a)(-3,-2) b)No solution c)(2,3) d)(-1,1)

Find all complex solutions for the following equation by hand. 4/(x+1) - 8/(x-1) = 8x/(1-x^2)

Which function has been compressed vertically as one of its transformations? a)y=2/3(x-4)^1/2 b)y=-2^(x+1) - 10 c)y= log0.5 (x+4)-1 d)y = 7/4(x+4)² + 15

In 1975, ten students were suspected of putting a car in the gym of the High School. Mr. Brown, the school's principal, called all ten students in to his office and asked them if they helped to put the car in the gym. Explain what type of bias is involved in this situation?

Write as a radical and simplify. x⁵/⁶

Two sisters went to a candy shop. Angie bought 9 pounds of peach rings and 1 pound of licorice for $61. Next, Valene boul 5 pounds of peach rings and 1 pound of licorice for $37. How much does each candy cost per pound? Write a system of equations and solve. Peach rings cost per pound__.Licorice cost per pound__.

A business owner receives a $5,000 loan with 13% interest, charged at the end of each year. Write an expression to represent the amount owed, in dollars, after the given number of years of making no payments: a. after 1 year b. after 2 years c. after t years Explain how to convince someone that your expression for t years is correct.

The ratio of the weight of an object on Planet A to the weight of the same object on Planet B is 100 to 3. If an elephant weighs 4600 pounds on Planet A, find the elephant's weight on Planet B. The elephant's weight on Planet B is _____ lb.

A store sells CDs at one price and DVDs at another price. The figure below shows the revenue (in dollars) of the music store as a function of the number, c, of CDs and the number, d, of DVDs that it sells. What is the price of a CD? $... What is the price of a DVD? $....

Solve the following inequality and graph the solution set. |5/6 x- 5| > 10 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is an interval. The solution is (Simplify your answer. Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) B. The solution is one or two points. The solution set is (Type an integer or a fraction. Use a comma to separate answers as needed.) C. The solution set is Ø.

A pendulum swings a length of 36 inches on its first swing. Each successive swing is of the preceding swing. Find the length of the fourth swing and the total length swung during the first four swings. The length of the fourth swing is in. (Round to the nearest tenth as needed.) The total length swung during the first four swings is in. (Do not round until the final answer. Then round to the nearest tenth as needed.)

A high school wants to estimate the number of students who plan to see the next school play. Which of the following samples would best represent the entire population of students at the high school? 1. 50 students are randomly selected at the previous school play. 2. 50 students are randomly selected from the sophomore class. 3. 50 students are randomly selected during a meeting of the school's drama club. 4. 50 students are randomly selected during an all-school assembly. Eddie and Fred want to estimate the mean amount of time people spend at their local shopping mall. They each randomly select people as they leave the mall and ask how much time they spent there. Here are the results, given in minutes:

If a₁ = 4 and aₙ = 3aₙᐨ ₁+3 then find the value of a₄.

Find the seventh term of the geometric sequence 24, 8, 8/13 a₇ = (Simplify your answer. Type an integer or a simplified fraction.)

Find the sum of the first four terms of the sequence. 4, 4/5, 4/25 S4= (Simplify your answer.)

Solving the following equation will require you to use the quadratic formula. Solve the equation for θ between 0 and 360°, and round your answers to the nearest tenth of a degree. (Enter your answers as a comma-separated list.) cos² θ + sin θ = 0

Consider the function f(x) = 2,139(1.075)⁸. What does the 8 represent? 1. The starting value 2. The function is growing at a rate of 8% 3. The total amount of money and interest 4. The number of years the money is invested

Given the following set of functions: f (x) = 2x g(x) = x - 2 h(x)=x² Evaluate: g(3) , Choose the correct answer. (a) 3 (b) 9 (c) 1 (d) 6

The height (in feet) of a punted football is a function of the time the ball is in the air. The function is defined by the equation below. What is the height of the ball after 4 seconds? h(t): = -7t² + 48 t 1. 48 feet 2. 80 feet 3. -304 feet 4. 97 feet

Which is the equation of a hyperbola with co-vertices at (0, 7) and (0, -7) and a transverse axis that is 12 units long? (a) (y³/36)-(x²/144)=1 (b) (x²/144)-(y³/49)=1 (c) (y³/14)-(x²/144)=1 (d) (x²/36)-(y³/49)=1

Which inequality best represents the domain of the function shown on the graph?

At the beginning of a population study of fish, a colony has 19,654 fish. The fish population increases by 5.6% yearly. Let t be the number of years since the start of the study. Let y be the population of fish. Which exponential function shows the relationship between y and t? y(t) = 19,654(1.056)^t y(t) = 19,654(0.944)^t y(t) = 5.6(19,654)^t y(t) = 94.4(19,654)^t

Find the range of the function h(w)= 19-3w for the domain {-4, -1, 2, 5} 1. {-34, -25, -16, -7} 2. {7, 15, 25, 34} 3. {4, 13, 22, 31 } 4. {-5, -2, 1,4}

Given f(x)=x² + 3x-4 Name the y-intercept 1. (-1.5, -6.25) 2. (-4,0) 3. (0, -4) 4. (-4,1)

Solve the following Bernoulli equation dy/dx+ y/x-2= 5(x-2)y¹/². Do not put an absolute value in your integrating factor.

△CUT = △RAT Given: B is the midpoint of AE LA = LE LCBA = LDBE

(a) Make a scatter plot for the data presented in the table. x -2 -2 -1 0 1 1 1 2 2 3 y 2 3 2 1 0 1 -1 -1 -2 -2 (b) Draw the line of best fit on your scatter plot above.

Find c if a 2.82 mi, b = 3.23 mi and ZC = 40.2 degrees. Enter c rounded to 3 decimal places. Assume LA is opposite side a, ZB is opposite side b, and ZC is opposite side c.

Given y = (3x - 5)(x + 8), what are the zeros of this function? 1. 5 and -8 2. 5/3 and -8 3. -5 and 8 4. 5/3 and 8

A rocket is shot off from a launcher. The accompanying table represents the height of the rocket at given times, where x is time, in seconds, and y is height, in feet. Write a quadratic regression equation for this set of data, rounding all coefficients to the nearest tenth. Using this equation, find the height, to the nearest foot, at a time of 9.3 seconds. Time in Seconds (x) Height in Feet (y) 0.8 243 1.4 412 2.2 626 2.8 769 3.8 983 5 1172

This table represents function f. x -3 -2 -1 0 1 2 3 f(x) -4.5 -2 -0.5 0 -0.5 -2 -4.5 If function g is a quadratic function that contains the points (-3,5) and (0,14), which statement is true over the interval [-3,14] The average rate of change of f is the same as the average rate of change of g The average rate of change of f is more than the average rate of change of g The average rate of change of f is less than the average rate of change of g. The average rates of change of fand g cannot be determined from the given information

Find the exact value of each trigonometric function (no decimals!). 1. cos135° 2. tan 240° 3. sec120°

In the ________ pair (2.37, 5.42) the x-________is 2.37 and the y-coordinate is 5.42. The _____of a line is a ratio (fraction) that compares the vertical change with the corresponding horizontal change as we move along the line from one point to another. A slope triangle is a______ triangle that can be drawn on a straight line to determine the____ and the horizontal change, called the vertical change, called the An average______ of change describes how much one quantity changes with respect to another. The point where a line intersects the y-axis is called the y-_____ of the line. Two examples of______ equations in two variables are û = -50.8 +2.3x and y' = 89.2+3.045x. They are called this because their graphs are lines. The___ form of an equation of a line that is used in algebra is y=mx+b.. Linear equations in two variables can be used to mathematically describe, or____ real-world situations.

Consider function h h(x)= { 3x-4 x<0 2x- 3x+ 10 0≤x<4 2ˣ x≥4} What are the values of the function when I = 0 and when = 4? A(0) = 10 A(4) = 16

Find the general power series solution centered at Xo=0 for the differential equation y' - 2xy = 0

Find a₁₀ given the geometric sequence -2, 6, -18, 54, ... a₁₀ = 80 a₁₀ =890 a₁₀ =45000 a₁₀= 39366

A new amusement park presold discounted tickets for the opening day as well as upon arrival at the park. The opening day ticket sales for the park, including presales, is represented by this function, where T(A) is the number of tickets sold h hours after opening at 7:00 a.m. T(A) = (386 + 110h)/h What is the approximate rate of change in the number of tickets sold between 10:00 a.m. and 1:00 p.m.? (A) -21 tickets per hour (B) -110 tickets per hour (C) -64 tickets per hour (D) -39 tickets per hour

Write the series with summation notation. 3+7+11+15+19 3+7+ 11 + 15 +19= Σ?

Write the first four terms of the arithmetic sequence with a₁ = 2 and 12th term is -31. Write an equation to find the nth term.

Solve the given equation for x. 6⁵ˣ-⁵ = 46 You may enter the exact value or round to 4 decimal places.

Express using rational exponents. (Assume the variable is a non negative real number.) 6√y²

Suppose A = 1 1 -1 2 1 0 1 -1 0 , Finding the inverse matrix.

Let & be the line of equation (x,y)= (2,1) + t(4,3). And let Q=(-4,9) be a point in the plane. The distance from point Q to the line is:

Solve √ (-5x +4)= x + 2 Do not include x = in your answer. If there is no solution, the answer is the empty set Ø

Which function defines ( ÷ g)(1) f(x) = (3.6)*+2 g(x) = (3.6) 31+1 A (J + g)(z) = (1.8)~2z+3 B. (g)(x) = (1.8)38²+7+2 c. (g)(x) = (3.6)45+3 D. (g)(x) = (3.6)-20+¹

a) Find the inverse of the following function; y=2/(4X-1) b) Find the sum of the infinite geometric series: 1/2 - 1/4 + 1/8 - .....

The function f(x) = 3^x + 1 is shown above. Complete each of the following statements by dragging the best choice from the list at the bottom of the page. Some answers will remain after you have completed each statement. (1) The base value for this function is _____________ (2) The function f(x) = 3^x + 1 is a ___________ function. (3) The point _____________is the y-intercept of the graph. 4. The purple line on the graph is a ____________ and has an equation of ___________ (5) The domain of the function is ______________ (6) The range of the function is ______________