Sequences & Series Questions and Answers

Check all of the following that are geometric sequences 4 8 16 32 64 1 2 3 4 5 7 12 17 22 27 1 3 9 27 81

For what value of k will the polynomial p x 4x 3x kr 2 have the same remainder when it is divided by x 1 and x 3 a 34 b 30 Oc 140 d 132

5 Find the sum of the arithmetic sequence with 5 d 3 and n 22

5 Find the sum of the geometric sequence 10 n 1 3 4 1

1 Which lists four consecutive terms in ar arithmetic sequence A 4 8 16 32 C 4 7 10 13 B 4 4 2 2 D 4 9 16 2

Given the following sequence find a12 128 64 32 16 8

a F x t cos w t X w wo X w wo b F x t sin wot j x w wo X w wo c F sgn t 1 jw 1 where sgn t t 0 1 t 0 d F 1 2nd w refers to the signum function

Ba Consider the infinite geometric sequence 162 54 18 6 Find the common ratio Enter your next step here

On January 2001 a company takes a 19 000 000 Loan to purchase an apartment complex The loan is to be financed over 8 years at an interest rate of 7 25 payable every six months a What is the periodic payment on the loan b What is the total amount interest paid after two years C How much of the Principal amount of the loan is yet unpaid

Find g f 2 23 1 GWNO W Show Transcribed Text 3 MINIT X P x X 0 8 graph piecewise function

Consider the geometric series 64 16 4 Find the sum of the first 5 terms S5 de Enter your next step here JE OD W b 7

Find i 1 23 i 1 i 1 i 1 JE CO I ab Enter your nex 0

10a 1 Consider the infinite geometric sequence 2 2 r Determine the common ratio r between consecutive terms Enter your next step here h 1 8 7 1 32

You are choosing between two different cell phone plans The first plan charges a rate of 24 cents per minute The second plan charges a monthly fee of 29 95 plus 10 cents per minute How many minutes would you have to use in a month in order for the second plan to be preferable Round up to the nearest whole minute minutes

You need 450 mL of a 70 alcohol solution On hand you have 60 alcohol mixture You also have 90 alcohol mixture How much of each mixture will you need to add to obtain the desired solution You will need mL of the 60 solution

Y Write an equation for the graph below in terms of 11 Fo 3 2

7 6 5 3 2 1 7 Slope m 9 5 3 2 2 N 3 4 S 6 7 1 2 3 4 5 Find the slope of the line a Enter your answer as an integer or as a reduced fraction in the form A B

Using the graph provided determine the slope of the line shown 7 6 5 4 NWA in 3 2 8 7 6 5 4 3 2 10 1 2 3 2 3 497 09 4 8 678

exponential form Assume that the radicands represent positive real numbers 10 7 5 14 107 5 14

9 The owner of a small restaurant bought 50 kilograms of rice Each week the restaurant uses 2 5 kilo grams of rice Function R gives the remaining amount of rice in kilograms as a function of the number of weeks w since the rice was purchased a Complete the table Weeks 6 12 W Amount of rice left kilograms Write a function rule to describe the situation w c Sketch the graph kilograms of rice remaining 90 80 70 60 50 40 30 20 10 2 4 6 8 weeks 10 12

7 The table and the graph show the population of a country between 2010 and 2015 year 2010 2011 2012 2013 2014 2015 population millions 36 5 37 7 38 2 38 4 38 9 39 1 s endod 8 39 2010 2011 2012 2013 a Find the average rate of population growth between 2011 and 2015 2014 2015

On a bicycle Salom rides for 7 hours and is 44 miles from her house After riding for 10 hours she is 62 miles away What is Salom s average rate over the last 3 hours of her trip miles per hour

Using sine Fourier Intergral representation of the function f x e x 0 we have S 00 asin ka 1 a where K 9 da

Simplify the expression to a polynomial in standard form 3x 10 x 2x 1

Find the length of a road section for each volunteer if there are the following numbers of volunteers of Volunteers 8 10 25 Length of Road

Find a number of incongruent solutions of the equation 8 0 mod 2015 cf 0155 x 13 x 31 Hint Use Legendre symbol

Consider the finite difference approximation f x f x 2h 16f x h 30f x 16 x h x 2h 12h 0 h Ife is the machine precision what is the best estimate for t 1 2 6 c 2

53 Solve for the unknown side X 12 Round your answer to the nearest tenth

Dox weighing 275 lb hangs from two cables as shown in the figure below Find the tension in each cable arry your intermediate computations to at least 4 decimal places Round your final answers to the nearest tenth Note that the ALEKS graphing calculator cam used to make computations easier 30 Platform 11th Tension in left cable Tension in right cable

The hourly wages for entry level positions at various firms were recorded by a labor research firm The results follow Starting Hourly Wages for 16 Companies 7 15 9 29 9 97 7 27 10 83 10 09 8 69 8 05 Find the first and third quartiles First quartile chird quartile raw a box and whiskers plot of the data 11 39 7 58 8 47 10 45 7 41 11 45 7 71 10 33

1 point Suppose V V2 V3 is an orthogonal set of vectors in R5 Let w be a vector in Span v1 U2 U3 such that V V 30 V V 11 V3 V3 1 W V1 then w 150 w V 55 w V3 1 V V V3

c To what limit s can the fixed point iteration In 5 cos n 1 2 1 krn 1 4 1 k converge as noo and for what values of k

In my Tae Kwon Do class there is a black belt four red belts one blue belt two green belts and four yellow belts If the sensel selects a student at random to lead the warm up find the probability as a reduced fraction that the person is Part 1 of 3 a Either a green belt or a yellow belt The probability that the student is either a green belt or a yellow belt is Part 2 of 3 b Either a black belt or a blue belt The probability that the student is either a black belt or a blue belt is Part 2 3 Part 3 of 3 DO DO X

The general manager of a fast food restaurant chain must select 5 restaurants from 17 for a promotional program How many different possible ways can this selection be done It is possible to select the five restaurants in different ways X 3

A poll was conducted of 2506 Americans who were employed full time about the gender gap in pay Half were men and half were women One question asked I believe men and women at my company are paid equally for equal work The number giving each response is shown below Response Agree Disagree Not sure 82 Part 0 3 Part 1 of 3 Men 990 788 181 379 86 Women a If a person who participated in the survey is selected at random what is the probability that he or she disagreed Write as a decimal rounded to two decimal places The probability that he or she disagreed is approximately X 5

3 Functions A t and B t give the height of student A and Student B respectively t years after they are born In each function height is measured in feet Key Here are the graphs of the two functions a Which function value is greater A 2 or B 2 b Identify which values of t make the equation A t B t true Height feet c Identify at least 2 values of t at which the inequality A t B t true 8 9 10 Years 2 A 11 12 13 B 14 15 16

A fast food restaurant has a cost of production C z 11z 105 and a revenue function R z 6r When does the company start to turn a profit Enter the exact answer If there is no solution enter NS If there is an infinite number of solutions enter IS

O Vertical stretch by 2 followed by a translation 3 units right O Vertical stretch by 2 followed by a translation 3 units down O Vertical stretch by 2 followed by a translation 3 units up O Vertical stretch by 2 followed by a translation 3 units left Question 7 Describe the transformation of f x x represented by g x x 11 4 O Translation 1 unit down and 4 units right by g x 2x 3 O Translation 1 unit left and 4 units down O Translation 1 unit right and 4 units up

d 5 marks 0 f 5 marks e 10 marks x 3 x 2 0 dax 2 2 2x4x 4x 2x 1dx d x x 2

Let vectors v 9 12 and w 5 12 be given Determine the vectors X v 2w and y V W Find the angle between the vectors v and w Find a vector z of length 20 that makes equal angles with the vectors v and w Is the vector z unique Explain Also plot the vectors v w x y z on one graph

For each function state whether it is linear quadratic or exponential Function 1 x 3 4 5 6 7 y 9 13 17 21 25 Linear Quadratic Exponential None of the above Function 2 X 0 1 2 3 4 y 8 16 32 64 128 Linear Quadratic Exponential None of the above Function 3 X 4 5 6 7 8 y 55 39 26 16 9 Linear Quadratic Exponential None of the above

You want to restrict the domain of the function shown in the graph below to make it one to one so that it will have an inverse What domain in interval notation could you use Select all correct answers Coldet all th 8 7 6 5 41 3 1 0 8 7 6 5 4 3 2 1 1 2 3 0 1 2 3

Find tane cose and esce where e is the angle ahown in tpur Give approximations 7 124

Bank 02 03 C1 The total cost b x in dollars for renting a bowling lane for x hours is shown b x 3x 15 What does b 3 represent The number of dollars it costs to rent the bowling lane for 3 hours The number of games you can bowl in 3 hours The number of games you can bowl for a cost of 3 The number of hours the bowling lane can be rented for a cost of 3

The number of bacteria P h in a certain population increases according to the following function where time h measured in hours P h 2800e0 06 h How many hours will it take for the number of bacteria to reach 3300 Round your answer to the nearest tenth and do not round any intermediate computations hours X 5

Espa Suppose that the dollar value v t of a certain house that is t years old is given by the following exponential function v t 532 000 1 04 Find the initial value of the house 0 Does the function represent growth or decay Ogrowth C decay By what percent does the value of the house change each year TE D

Abdul launches a rocket straight up into the air The table below gives the height H t of the rocket in meters few times t in seconds during its flight Time t seconds 0 2 8 5 6 8 4 11 2 Height H t meters 0 84 140 42 0 a Find the average rate of change for the height from 0 seconds to 5 6 seconds meters per second b Find the average rate of change for the height from 8 4 seconds to 11 2 seconds meters per second E

Jane is driving a racecar The table below gives the distance D t in meters she has driven at a few times t seconds after she starts Time t seconds 0 2 5 7 9 Distance D t meters 0 78 6 151 5 205 1 255 9 a Find the average rate of change for the distance driven from 0 seconds to 2 seconds meters per second b Find the average rate of change for the distance driven from 7 seconds to 9 seconds meters per second

Bob is cooking a roast The table below gives the temperature R t of the roast in degrees Celsius at a few time in minutes after he removed it from the oven Time t minutes 0 10 30 50 70 Temperature R t C 226 6 205 6 157 6 119 6 61 6 a Find the average rate of change for the temperature from 0 minutes to 30 minutes C per minute b Find the average rate of change for the temperature from 50 minutes to 70 minutes C per minute U Jal A

A study is done on the number of bacteria cells in a petri dish Suppose that the population size P 1 after 1 hours given by the following exponential function P t 2500 0 75 Find the initial population size Does the function represent growth or decay growth decay By what percent does the population size change each hour n C 121