Sequences & Series Questions and Answers

Solve the system of equations graphically. y = 3x + 10 y=-6x-26 Select the correct answer below and, if necessary, fill in any answer boxes to complete your choice. A. The solution of the system of equations is x = and y= B. There are infinitely many solutions. C. There is no solution.

For each sequence, decide whether it could be arithmetic, geometric, or neither. a. 25, 5, 1,... b. 25, 19, 13,... c. 4, 9, 16,... d. 50, 60, 70,... e. 1, 3, 18,... For each sequence that is neither arithmetic nor geometric, how can you change a single number to make it an arithmetic sequence? A geometric sequence?

A geometric sequence g starts 80, 40,... amaldon saitased no a. Write a recursive definition for this sequence using function notation. b. Use your definition to make a table of values for g(n) for the first 6 terms. c. Explain how to use the recursive definition to find g(100). (Don't actually determine the value.)

A piece of paper has an area of 96 square inches.. a. Complete the table with the area of the piece of paper A(n), in square inches, after it is folded in half n times. b. Define A for the nth term. c. What is a reasonable domain for the function A? Explain how you know.

Sam and Drew decide to mow lawns during their summer break with different companies. Sam gets a flat $15.00 every day plus $8.00 for every yard he mows. Drew gets paid $45.00 daily plus $6.00 for each yard he mows. When will they have mowed the same number of yards and earned the same amount? How much will they have earned?

List the first 4 terms of this sequence. 2) Write an expression to represent f(20). 3) A person is trying to quit chewing gum. They decide they will have 64 pieces in week 1, but each week have half as many as the week before. The function f represents the number of pieces of gum they will have in week n. What is a reasonable domain for this function? Explain your reasoning.

I.A-Directions: Find the next three terms of the given sequences 1.-7,-9,-11,-13.-15-17-19 2. 3.2, 4.3, 5.4,6-5, 7-6,87 I.B. Write the first three terms of the sequence whose nth term is given by the rule. 1. an=2n-1 2. an=3n 3. an-8-2n

On January 1, 2010, Allison put 1 penny into her piggy bank. Each month, she put 3 more pennies into her piggy bank than she put the previous month. How many pennies did Allison put into her piggy bank in December 2015? O 13 O 16 O 178 O 214 ning to our Cookie Policy. Accep

Determine if the sequence with the following pattern: 1.25, 2.5, 5, 10, 20, ... is arithme O The sequence is geometric. O The sequence is arithmetic. The sequence is neither arithmetic nor geometric

Find the 10th partial sum of the sequence 6144, -3072, 1536, -768... O 12,276 O 4,104 O 12,264 O 4,092

Let p, q, r be positive integers such that q/p is an integer if p, q, r are in geometric progression and the arithmetic mean of p, q, r is q+5, also x=p² - p + 14/p+1 Then [x] is, where [.] denotes greater integer function. A-19 B-14 C-6 D-15

Write the first five terms of the sequence. f(0) = 8: f(n) = f(n-1) + 3 f(0) f(1) = f(2)= f(3) = ƒ(4) -

Graph f(x) = -5x. Use the graphing tool to graph the function.

Sasha went to a champagne brunch and had several glasses of champagne. She estimated her blood alcohol level was 0.12. She knows a safe driving level for someone of her weight is 0.03. If the blood alcohol level decreases by 25% every hour, how long does she need to hang out with her friends (without drinking any more alcohol) before it is safe for her to drive?

A tennis ball bounces on the ground n times. The heights of the bounces, h₁, h2, h3,..., hn, form a geometric sequence. The height that the ball bounces the first time, h₁, is 80 cm, and the second time, h2, is 60 cm. (a) Find the value of the common ratio for the sequence. (b) Find the height that the ball bounces the tenth time, h10 (c) Find the total distance travelled by the ball during the first six bounces (up and down). Give your answer correct to 2 decimal places.

The 1st, 5th and 13th terms of an arithmetic sequence, with common difference d. d + 0. are the first three terms of a geometric sequence, with common ratio r. r 1. Given that the 1st term of both sequences is 12. find the value of d and the value of r.

Here are the values of the first 5 terms of 3 sequences: A: 30, 40, 50, 60, 70, . . . B: 0, 5, 15, 30, 50, . . . C: 1, 2, 4, 8, 16, . . . If the patterns you described continue, which sequence has the second greatest value for the 10th term? Great Job! A B C Explain your thinking.

A sequence of numbers follows the rule: multiply the previous number by -2 and add 3. The fourth term in the sequence is -7. a. Give the next 3 terms in the sequence. b. Give the 3 terms that came before -7 in the sequence.

Match each sequence with one of the recursive definitions. Note that only the par the definition showing the relationship between the current term and the previo term is given so as not to give away the solutions. A. 3, 15, 75, 375 B. 18, 6, 2, C. 1, 2, 4,7 D. 17, 13, 9, 5 1. a(n) = a(n-1) 2. b(n) = b(n-1)-4 3. c(n) = 5 c(n-1) 4. d(n)= d(n-1)+n-1 .

Penn stacks all of his snowballs in a square pyramid. The number of snowballs, P(n), in n layers of the square pyramid is given by P(n)=P(n-1) + n². Which could not be the number of snowballs Penn has? OA. 5 OB. 14 O C. 30 OD. 25

What is the explicit formula for the geometric sequence with this recursive formula? a1=-6 an=an-1*1/4 A. 3, --4. (1) (-¹) = O B. , -• (-4) (-1) 6 C O C. an C. a ²n = 1/1 • (-6) (²-1) D. an -6. (1)-1) =

Many credit card companies charge a compound interest rate of 1.8% per month on a credit card balance. Miriam owes $550 on a credit card. If she makes no purchases or payments, she will go more and more into debt. Which of the following sequences describes her increasing monthly balance? OA. 550.00, 559.35, 568.86, 578.53, 588.36,... B. 550.00, 559.90, 569.80, 579.70, 589.60,... OC. 550.00, 649.00, 765.82, 903.67, 1,066.33, ... D. 550.00, 550.99, 551.98, 552.98, 553.97,... E. 550.00, 559.90, 569.98, 580.24, 590.68, ...

Two large numbers of the Fibonacci sequence are F(49) - 7,778,742,049 and A(50) = 12,586,269,025. If these two numbers are added together, what number results? A. F(51) B. F(99) C. F(52) D. F(54)

Ahmed is working at a burger joint. His boss pays him $6.50 per hour and promises a raise of $0.25 per hour every 6 months. Which sequence describes Ahmed's expected hourly wages, in dollars, starting with his current wage? OA. 0.25, 0.50, 0.75, 1.00, 1.25,... B. 6.50, 13.00, 19.50, 26.00, 32.50, ... C. 6.50, 6.25, 6.00, 5.75, 5.50, ... D. 6.75, 7.00, 7.25, 7.50, ... OE. 6.50, 6.75, 7.00, 7.25, 7.50, ...

A particular strain of bacteria triples in population every 45 minutes. Assuming you start with 50 bacteria in a petri dish, how many bacteria will there be in 4.5 hours? O A. 7015 OB. 36,450 O C. 12,150 OD. 33,960

Ezra is training for a track race. He starts by sprinting 100 yards. He gradually increases his distance, adding 5 yards a day for 21 days. The explicit formula that models this situation is an = 100 + (n-1)5. How far does he sprint on day 21? A. 200 yards B. 100 yards C. 225 yards D. 205 yards

Select the answers that best complete the given statements. A sequence in which each term after the first differs from the preceding term by a constant amount is called a/an geometric sequence The difference between consecutive terms is called the constant factor of the sequence.

The sequence given is defined using a recursion formula. Write the first four terms of the sequence. a₁ = 2 and an = 3an-1 for n≥2

There are 13 left-handed and 21 right-handed spirals on the cacti in the photograph. What is special about these numbers? A. They are consecutive terms in the Fibonacci sequence. B. The value of the 13th term of the pyramidal sequence is 21. C. The value of the 13th term of the Fibonacci sequence is 21. D. They are consecutive terms in the pyramidal sequence.

The general term of a sequence is given. Determine whether the sequence is arithmetic, geometric, or neither. If the an = n²+2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The sequence is geometric with a common ratio of B. The sequence is arithmetic with a common difference of C. The sequence is neither arithmetic nor geometric.

Simplify each expression so it is written as only one exponential expression. Do not evaluate to a number. Example: 10² x 10² = 104 a. 103 x 104 107 o b. 102x 10-9- c. 105 x 10-6- d. 10 10-7✓ o 10³ 10³ 10-11 10-2 X = 10³ x 1010x

Determine if the finite correction factor should be used. If so, use it in your calculations when you find the probability. In a sample of 700 gas stations, the mean price for regular gasoline at the pump was $2.861 per gallon and the standard deviation was $0.008 per gallon. A random sample of size 55 is drawn from this population. What is the probability that the mean price per gallon is less than $2.858? The probability that the mean price per gallon is less than $2.858 is (Round to four decimal places as needed.)

A hiker on the Appalachian Trail planned to increase the distance covered by 20% each day. After 7 days, the total distance traveled is 51.664 miles. Part A: How many miles did the hiker travel on the first day? Round your answer to the nearest mile and show all necessary math work. Part B: What is the equation for Sn? Show all necessary math work. Part C: If this pattern continues, what is the total number of miles the hiker will travel in 10 days? Round your answer to the hundredths place and show all necessary.

An applicant receives a job offer from two different companies. Offer A is a starting salary of $58,000 and a 3% increase for 5 years. Offer B is a starting salary of $56,000 and an increase of $3,000 per year. Part A: Determine whether offer A can be represented by an arithmetic or geometric series and write the equation for An that represents the total salary received after n years. Justify your reasoning mathematically. (3 points) Part B: Determine whether offer B can be represented by an arithmetic or geometric series and write the equation for B, that represents the total salary received after n years. Justify your reasoning mathematically. (3 points) Part C: Which offer will provide a greater total income after 5 years? Show all necessary math work. (4 points)

Use the Root Test to determine whether the series converges. 1/14 + (1/28)2 + (1/42)3+ (1/56)4 +... Select the correct choice below and fill in the answer box to complete your choice. A. The series converges because p = B. The series diverges because p = C. The Root Test is inconclusive because p =

. Which of the following is true? I. The series -2, 4, 8, 16,... is a geometric sequence. II. The series √√2, 2, 2√2, 4,... is a geometric sequence. 2 2 3 9 27 III. The series 2, (A) I only (B) II only **** is a geometric sequence. (C) I and II only (D) II and III only (E) I, II, and III

At a bowling alley, the cost of shoe rental is $2.75 and the cost per game is $4.75. If f (n) represents the total cost of shoe rental and n games, what is the recursive equation for f (n)? Of(n) = 2.75 +4.75 + f(n-1), f(0) = 2.75 Of(n) = 4.75 + f(n-1), f(0) = 2.75 Of(n) = 2.75 +4.75n, n > 0

Determine whether the following series converges. 00 k=2 K²2² +1 Let a 20 represent the magnitude of the terms of the given series. Select the correct choice below and fill in the answer box(es) to complete your choice. OA. The series converges because a OB. The series diverges because ax = OC. The series converges because a = OD. The series diverges because ax O E. The series diverges because ak OF. The series converges because ax = is nonincreasing in magnitude for k greater than some index N and lim ax = k-00 is nonincreasing in magnitude for k greater than some index N. and for any index N, there are some values of k>N for which ax+128, and some values of k>N for which ak+15ak and for any index N, there are some values of k>N for which ax+12ax and some values of k>N for which ak+158k is increasing in magnitude for k greater than some index N and lim ax = k-0 is nonincreasing in magnitude for k greater than some index N.

4.7.PS-11 Two communications companies offer calling plans. With Company X, it costs 25¢ to connect and then 5¢ for each minute. With Company Y, it costs 15¢ to connect and then 4¢ for each minute. Write and simplify an expression that represents how much more Company X charges, in cents, for n minutes. Which of these expressions represents how much more Company X charges than Company Y? OA. (25n-4)-(15n-5) OB. (25+5n)-(15+4n) OC. 25n-5-15n-4 OD. (25+4n)-(15+5n) dial Chock Answer.

6. The population of a city started at 378,000. Every year thereafter it decreased by 23,000 individuals a. Represent the first five terms of the sequence using a table of values SEQUENCES b. Describe the domain and the range of the sequence SEQUENCES: Post-Test c. Write a recursive and an explicit formula to represent the pattern shown in your table. d. Use your formulas to predict the population of the city after a decade.

The population of a city started at 378,000. Every year thereafter it decreased by 23,000 individuals. a. Represent the first five terms of the sequence using a table of values b. Describe the domain and the range of the sequence c. Write a recursive and an explicit formula to represent the pattern shown in your table d. Use your formulas to predict the population of the city after a decade

Jason is saving up to buy a digital camera that costs $490. So far, he saved $175. He would like to buy the camera 3 weeks from now. What is the equation used to represent how much he must save every week to have enough money to purchase the camera?

What can you say about the series an in each of the following cases? (a) lim 816 an O absolutely convergent O conditionally convergent divergent cannot be determined ant1 an+1 = 4 (b) lim 816 an O absolutely convergent conditionally convergent an+1 = 0.6 O divergent O cannot be determined lim 816 an O absolutely convergent O conditionally convergent O divergent = 1 cannot be determined

Test the series for convergence or divergence. (-1)" n67 n=1 Identify b X Evaluate the following limit. lim bn n18 ince lim b = 318 0 and bn + b for all n, the series is convergent ✓ If the series is convergent, use the Alternating Series Estimation Theorem to determine how many terms we need to add in order to find the sum with an error less than 0.0001? X terms

Consider the following geometric series. Σ Find the common ratio. Determine whether the geometric series is convergent or divergent. convergent divergent

Consider the following geometric series. 2 + 0.5 + 0.125 + 0.03125 + ... Find the common ratio. |r| = Determine whether the geometric series is convergent or divergent. convergent divergent If it is convergent, find its sum. (If the quantity diverges, enter DIVERGES.)

7. A theater has 30 rows of seats. The first row contains 20 seats, the second row contains 21 seats, and so on, such that each row has one more seat than the previous one. Write the explicit formula for this situation and use it to determine how many seats are in row 30. (2 points)

Given the sequence 34, 42, 50, 58, 66,..., find: a) The next term in the sequence. b) The recursive formula. c) The explicit formula. d) The 10,000th term in the sequence.

Write the terms a₁, 82, 83, and as of the following sequence. If the sequence appears to converge, make a conjecture about its limit. If the sequence diverges, explain why. an = 1/12^n, n = 1,2,3.

Rakesh and Tessa were asked to find an explicit formula for the sequence 100, 50, 25, 12.5,..., where the first term should be f(1). Rakesh said the formula is f(n) = 100. (1/2)^n-1 and Tessa said the formula is f(n) = 200.(1/2)^n-1 Which one of them is right? Only Rakesh Only Tessa Both Rakesh and Tessa