100 points plz answer with a compete answer or you will get reported :) 1. Describe and extend each sequence.
A. The height, in feet, of windowsills in a high-rise building is represented by this sequence:
3, 15, 27, 39, ...
Describe the rule for the sequence.

Find the next two terms of the sequence. Show your work.

B. Mason put sticky notes on some pages of his math book. The page numbers form this sequence:
3, 5, 8, 13, 21, 34, ...
Describe the rule for the sequence.

Find the next two terms of the sequence. Show your work.

THE EXPLICIT FORMULA
2. Use the following arithmetic sequence and the formula an = a1 + (n – 1)d to answer the questions below.
123, 116, 109, 102, 95, ...
Part I: Find the value of each of the following:
a1 = and d =
Part II: Find the explicit formula. Show your work.

Part III: Use the explicit formula you found in Part II to find the value of the 100th term in the sequence, a100. Show your work.

3. State whether each sequence is arithmetic or geometric, and then find the explicit and recursive formulas for each sequence. (10 points: 5 points each)
Formulas:

Part I: The total value of a collection of nickels can be described by this sequence:
5, 10, 15, 20, 25, 30, ...
Type of sequence:

Explicit formula:

Recursive formula:

Part II: The number of rats living in an abandoned building increases each year. The total number of rats can be described by this sequence:
2, 6, 18, 54, 162, ...
Type of sequence:

Explicit formula:
Recursive formula:

4. A stone nudged off the Royal Gorge Bridge near Cañon City, Colorado, falls 1053 feet before hitting water. Because its speed increases as it falls, the distance it travels each second increases. During the first second, it drops 16 feet. During the next second, it drops an additional 48 feet. During the third second, it drops another 80 feet. The distances traveled each second form an arithmetic sequence:
16, 48, 80, ...
Part I: How far does the stone fall during the 5th second? Find and use the explicit formula.
What is the first term of the sequence?
What is d, the common difference?
Write the explicit formula in function notation. Use f(n) = f(1) + (n – 1)d, where f(1) represents the first term.
Use the explicit formula to find the distance the stone travels in the 5th second.

Part II: The table below shows the values in the sequence you already know. Use the explicit formula or the common difference to complete the table for the first 7 seconds.
Time (s) 1 2 3 4 5 6 7
Distance (ft) 16 48 80 144
Part III: Use the table from part II to answer the questions.
The values in the table form a(n) sequence.
The term values are shown in the row, and the term numbers are shown in the row.
This sequence is associated with a(n) function.
The domain of the function is the set of time values: .
5. Your track coach is letting you choose between two different workouts.
A: Run 10 minutes on Monday and double that time every day through Friday.
B: Run 30 minutes on Monday and add 10 minutes every day through Friday.
What type of function is represented by plan A? By plan B? Which plan should you choose if you have plans Friday night and want a short workout on Friday? Why? Create a table to justify your answer.
Plan A: function
Plan B: function
I would choose plan because .
Plan A minutes Plan B minutes
Monday
Tuesday
Wednesday
Thursday
Friday
6. Prove that linear functions grow by equal differences over equal intervals.
Part I. This is the graph of . Use the graph to show that equal intervals of x-values have equal differences of y-values.

a) Think about an interval on the x-axis starting with p and ending with p + k. What is the difference between the x-values? What is the difference between the y-values for these x-values? Complete the tables using .
Interval between p = 2 and p + k = 6 Difference
x-value 2 6 4
y-value –2

Interval between p = 10 and p + k = 14 Difference
x-value 10 14
y-value
b) The difference in the x-values for each interval is . This value is constant because
difference = (p + k) – p = .
c) The difference in the y-values for each interval is . This value is also constant because
\begin{aligned} \text{difference } &= -\frac{1}{2}(p + k) + 10 - (-\frac{1}{2}p + 10) \\ &= -\frac{1}{2}p - \frac{1}{2}k + 10 + \frac{1}{2}p - 10 \\ &= -\frac{1}{2}k \end{aligned}
difference
​
=−
2
1
​ (p+k)+10−(−
2
1
​ p+10)
=−
2
1
​ p−
2
1
​ k+10+
2
1
​ p−10
=−
2
1
​ k
​
d) Does your answer in part c depend on p? If not, what does it depend on?

If a baby uses 15 diapers in 2 days, how many diapers will the baby use in a year?

Solve the problem. a student earned grades of c, a, b, and a in four different courses. those courses had these corresponding numbers of credit hours: 4, 5, 1, and 5. the grading system assigns quality points to letter grades as follows: a = 4, b = 3, c = 2, d = 1, and f = 0. compute the grade point average (gpa) and round the result to two decimal places. 3.40 3.50 8.75 2.18

1. spending nights at a 3 star hotel in paris, france or spending nights at a 5 star hotel in new york city. 2. cell phone plans, comparing monthly fee and price per text message. you must use basic phones for the purpose of this project. vacation situation: you have graduated from high school and you are planning to go on a vacation by yourself. you have always wanted to travel to paris, france, but you need to consider the price of the ticket as well as the cost of hotel per night. as an alternative, you want to look into spending the same number of nights in new york city at a luxurious 5 star hotel. now you need to determine whether you should go to paris which will cost you for flight and hotel or stay in nyc that will cost you only for the hotel. note: you are spending the same number of nights at each destination. assignment: gather information from travel agencies, such as american airline, orbitz, expedia, or kayak, through their website for cost of flight and cost of hotel. then write a system of linear equations for the two plans and create a graph. use the methods we have been studying to determine which plan is better based on the number of nights you decide to stay if you had $1500 to spend for this vacation. cell phone plans situation: you have graduated from high school and moved away to college. your parents have decided that it’s time for you to pay for your own cell phone. you have to stick to a strict budget. now you need to determine whether you should go with a plan that costs more per month but charges less per text message or a cheaper plan that charges more per message. assignment: you are to choose from a cellphone company that offers two talk and text plans. the company charges a monthly service fee of $20 for either plan the customer chooses: talk and text plan a charges five cents a minutes and twenty dollars for 250 texts. talk and text plan b charges ten cents a minute (first 100 minutes free) and fifteen dollars for 200 texts. note: assume you are purchasing a basic phone, which is $0 with 2-year contract. you cannot purchase unlimited text messaging for this exercise. use the methods we have been studying to determine which plan is better based on the number of text messages you send per month if you only have $75 to spend each month. project details you will decide which project you want to do. after you decide on a project, you will need to: 1) collect the data if necessary. 2) write the system of linear equations and a word problem once the data has been collected. 3) use the methods we have been studying (graphing and solving algebraically) to find the solution to the written system. 4) design the final display of the project on a poster board. be creative! project rubric 2 points = data for the scenarios. (only applicable to vacation plans) 1 points = data 1 points = sources documented 8 points = word problem and the system of equations 2 points = all variables are defined 6 points = both equations are accurate 8 points = graphic solution 4 points = each line is correctly graphed 2 points = labels and titles 2 points = point of intersection 8 points = algebraic solution and explanation 4 points = correct solving 2 points = explain your work and how you came up with the parameters 2 points = check 14 points = final project 4 points = creativity 4 points = contains the analysis of your equations 6 points = final product is organized and clear final project checklist – refer to the rubric above make sure you have the following items on your final project… • collected data (if necessary) • system of linear equations with variables defined • graphs of both equations (this can be done on desmos and printed or drawn by hand) • algebraic solution with work and units • analysis: o if you chose vacation plan: for how many nights are the prices going to be same? if you had $1500 to spend for your vacation, which plan would you choose and why? o if you chose talk and text plan: for how many minutes will both plans hare the same cost? if you had $75 to spend each month, which plan should you choose and why? vacation – data organizer 1) define the variables 2) complete the following chart to you come up with a systems of linear equations destination paris, france new york city hotel rating   name of hotel price of hotel (per night) compare same nights price of flight linear equation 3) write an equation for staying in paris, france. 4) write an equation for staying in new york, ny. talk and text plans – data organizer 1) define the variables. 2) express plan a as an equation. 3) express plan b as an equation. *make sure you take into consideration that first 100 minutes of talking on the phone is free!