Sequences & Series Questions and Answers

5 A Substance loses 25 of its total mass every 15 years If you start with 5mg of the substance how much will be present after 100 years

Points P and Q are connected to form a ray R True False

The Ferris wheel at the landmark Navy Pier in Chicago takes 7 minutes to make one full rotation The height H in feet above the ground of one of the six person cars can be modeled by 27 1 1 75 H t 70 sin t 1 75 80 where t is time in minutes Using H t for one full rotation this car s minimum height in feet is 1 150 2 70 3 10 4 0

What is an approximate average rate of change of the graph from x 5 to x 15 and what does this rate represent

25 Name the first five terms of the arithmetic sequence a 12 d 9 O21 12 3 6 15 O3 6 15 24 33 O12 21 30 39 48 O 3 12 21 30 39 12 3 6 15 24 O21 30 39 48 57 O None of these answers are correct

14 Find a34 if a 1 and d 2 O91 83 5 O 94 5 O 79 5 None of these are correct

12 Name the next two terms of the arithmetic sequence 35 50 65 80 O91 107 O 95 110 O96 108 O90 115

9 Find S7 of the sum of the geometric series a 32805 a7 45 r O 49196 O 49179 O 49212 O 49163 Mean

7 Name the first five terms of the arithmetic sequence a 38 d 3 O38 41 44 47 50 O38 35 32 29 26 41 38 35 32 29 O35 32 29 26 23 O41 44 47 50 53 O 35 38 41 44 47 O None of these answers are correct

4 Calculate the a67 term of the geometric sequence with a365 and r 1 05 O 36 O 67 O 36 O 67 O 5 Nens aft

3 What is Sn of the geometric series with a 64 r 3 and n 6 272 O 266 O 257 O 245 O236 O None of these are correct

14 Find S7 of the sum of the geometric series a1 39366 a7 3232 3 O 29551 O 29542 O 29518 O 29538 O None of these are correct 54 r

11 Find the sum of the geometric series a 81 a4 2187 r 3 S4

12 Find S4 of the sum of the geometric series a1 162 a4 6 r O 122 O 92 O 104 096 O None of these are correct 1 3

10 Find the sum of the geometric series 8 5 k 1 O97656 O97640 O97668 97625 O None of these are correct

4 Find the sum of the geometric series 9 5 2 3 x

2 Find the sum of the geometric series 9 5 1 2

4 For the geometric sequence find the two missing terms between 16 and 1024 16 1024

7 The following geometric sequence is missing four terms Identify any of the following answers that fit into this geometric sequence 448 1359 63 80 More than one answer may be correct select all that apply 28 15 20 112 45 02 1 None of these are correct

11 Find the next three terms in the geometric sequence 28 14 3 45 x

Find the first four terms of the geometric sequence a 27 r first four terms

2 Find the first four terms of the geometric sequence a1 16 7 4 first four terms x

45 X 1 X 2 NANIANIA y 1 MIN INMING 1 3 3 1 4 Show Transcribed Text

13 Find the sum of the arithmetic series if a 81 a26 19 and n 26 OS26 817 OS26 815 OS26 806 OS26 810 O None of these are correct

4 Find the sum of the arithmetic series if a 26 a28 163 and n 28 S28

Consider the sequence defined as follows a 1 1 a 2 2 a n a n 1 2 n n for n 2 a Determine the general formula for the nth term of the sequence b Find the sum of the first 100 terms of the sequence c Prove that the sequence is strictly increasing d Prove that the sequence is unbounded i e it does not have a finite limit

14 Find a45 if a 73 and d 3 2 O 126 O 131 5 O 139 O 137 m None of these are correct

5 21 Question 1 Let A 12 7 25 3 0 0 45 9 3 999 List all the elements of A that belong to each of the following sets a Natural numbers c Integers e Irrational numbers b Whole numbers d Rational numbers f Real numbers

What is the name of compound A H HO H CHO A CH OH A OH A D ribose B H B L talose C D threose D D xylose E L threose OC OH OE

Write as a radical and then simplify 8 Provide your answer below

he famous identity sin 0 cos 8 1 can be tweaked to produce the following A tan 0 sec 0 1 C none of these B 0 com 0 co 0 com M SELECT ALL

Solve 4x 5 2 x 2 Provide your answer below

H 5 MathBits com E D X Prove the following using the two column proof format GIVEN AE BD AC EC and BC DC PROVE AABC AEDC Statements 1 AE BD AC EC and BC DC 2 ZBCA ZDCE 3 BARC BEDE Reasons

D E C B be true DE EC AE EB AED XCEB E is the midpoint of DC

13 17 14 3 TOTA 1 How many students do not like either Handball or Volleyball 2 How many students only like Handball 3 How many students like Handball 4 How many students like Handball or Volleyball

Plot each point and form the triangle ABC Verify that the triangle ABC is a right triangle Find its area A 8 11 B 1 9 C 1 0 CA B www 17 OC Q To show that the triangle is a right triangle show that the sum of the squares of the lengths of two of the sides the legs equals the square of the length of the third side the hypotenuse Sum of the squares of the lengths of the legs of the triangle Square of length of the hypotenuse of the triangle Q G

3 The graph of a quadratic function is shown below Identify the vertex and write the axis of symmetry equation Draw and label the vertex and the axis of symmetry on the graph 76 54 b 2 J 2 11 3 4 5 6 7 3 Vertex ordered pair Axis of Symmetry Equation 4 For each of the graphs below determine the vertex and the axis of symmetry equation Identify the domain and range using interval notation a Vertex Axis of Symmetry Domain Range Vertex Axis of Symmetry Domain Range

Solve the system of equations by the elimination methoc 2x 8y 8 3x 7y 3

nd all solutions of the equation in the interval 0 2 Enter your answers as a comma separated list If there is no solution enter NO SOLUTION csc x cot x 3 TC 3 E T 5 3 X

1 Write each series using summation notation and find the sum of each series a 50 37 24 28 b NE 2 12 72 15 552

10 Meaghan just deposited 4000 in an account that pays 2 annual interest Write the equation and determine the account balance at the end of 5 years a It is compounded monthly b It is compounded continuously

8 Shannon is knitting a scarf with a pattern The first row has 8 red stiches and each subsequent row has 3 more red stitches than the row that precedes it for 14 rows a How many red stitches are in the 14th row b How many red stitches in total are in the 14 rows Sin ritin

2 Consider the series 18 3 1 1 a Is it arithmetic or geometric How do you know b Does it have a finite sum How do you know Find the sum

The new high intensity discharge HID headlights containing xenon gas have an expected life of 1900 hours Because a complete system costs 1000 it is hoped that these lights will last for the life of the car Suppose that the actual life of the lights could be 12 longer or shorter than the advertised expected life Write an inequality that gives the range of life of these new lights Let x be the expected life of the headlights What is the range of the expected life of the headlights hours

Use the graph of g to find g 4

A ball is thrown downward from the top of a 190 foot building with an initial velocity of 24 feet per second The height of the ball h after t seconds is given by the equation h 161 24t 190 How long after the ball is thrown will it strike the ground sec Round to the nearest tenth as needed BERE SERT REEE BARE REDE WERE 190 ft

b Using an appropriate triple integral evaluate the volume of Verify using Mathematica i ii z V1 x y r sin 0 Figure 1 z 3V1 x Figure 2 r cos 0 5 5 10ma

6 cm 3 cm 5 cm 6 cm 16 cm Find the surface area

We want to graph the function f x log4 x In a table below find at three points with nice integer y values no rounding and then graph the function at right Be sure to clearly indicate any asymptotes 4 points X log4 x 1 3 2 1 0 1 2 3 1 2 3 4 5 6 7 8 In words interpret the inequality x 81 7 the same way I did in the videos Note the words absolute value should not appear in your answer 2 points Solve the inequality and give your answer in interval notation Be sure to show all your work and writo postl work is oary to follow 14 pointel

Which decimal is equivalent to 9 Choose 1 answer A 2 8 B C D 2 8 2 889 26 2 9