CEMC's Open Courseware - Lesson 6: Bringing It All Together

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- - Try This
  - Combining Patterns
  - Finding the General Term
  - Extending Sequences
  - Alternative Format
- Review
- - Question 1
  - Question 2
  - Question 3
  - Question 4
- Practise
- - Exercises
  - Answers and Solutions
- Question Descriptions

Exercises

1. What would be the general term for the sequence represented by the following table?
  
  Term Number $1$ $2$ $3$ $4$
  
  Term Value $22$ $29$ $36$ $43$
2. How is the sequence in part a similar to the sequence represented in the following table? Can you use this to find the general term of the following sequence?
  
  Term Number $1$ $2$ $3$ $4$
  
  Term Value $-22$ $-29$ $-36$ $-43$
Roger was given a bank account containing $$ 500$ to use for his expenses. He takes $$ 30$ out of his account at the end of each week. After week $1$, Roger's account will contain $$470$.
1. Make a table of values for the money in the account over $5$ weeks.
2. Graph the values for the money in the account over $5$ weeks.
3. For how many months can he continue to take money out of his account at this rate? What tool would be most useful to solve this problem (a graph, a table, or the general term)?
Create an image pattern that corresponds to the expression $5\times n-2$ where $n$ is the image (or term) number.
Consider a sequence where the fourth term has a value of $66$ and the tenth term has a value of $108$. What is a possible general term of this sequence? Is there more than one answer?
To fix a car, George's Garage charges a base fee of $$ 60$ plus a fee of $$ 40$ per hour for the mechanic.
1. Let $t$ represent the number of hours required for the repairs. Display the cost of a repair job at the garage using a graph.
2. Use the graph to find a fair cost for a repair job that takes $2\dfrac{1}{2}$ hours.
3. If you paid $$240$ for the repairs, then how long was your car in the garage?
Yasmin wishes to get a cell phone plan. She has looked at two different plans as shown below:
Plan A: The base fee is $$10$ per month and there is a fee of $$0.30$ per call.
Plan B: The base fee is $$15$ per month and there is a fee of $$0.05$ per call.
1. Let $n$ be the total number of calls made. Write an expression showing the cost of making $n$ phone calls per month on each of the two plans.
2. Which plan would be best if you make $15$ calls per month? Would a table, a graph, or the general terms be helpful to solve this problem? Explain.
3. Is there a particular number of calls per month that would make the two plans equal in cost? Explain.
Cooking for larger numbers of people is more efficient, and cheaper, than for smaller numbers. For a particular meal at a banquet hall, it costs $$7.00$ to feed the first guest, $$6.90$ to feed the second guest, $$6.80$ to feed the third guest, and so on. For example, the cost of feeding a party of $3$ is $$7.00+$6.90+$6.80=$20.70$. This pattern continues with it costing $$0.10$ less to feed the "next guest," up to guest number $50$. If the banquet hall charges a fixed rate of $$14.95$ per guest, and there are $50$ guests at an event, then how much money is made at the event?
Consider the following image sequence.
1. Write an expression to represent the number of solid hexagons in terms of the number of dotted hexagons.
2. How many solid hexagons would be in the term that contains $42$ dotted hexagons?
3. How does the expression from part a) change if the sequence builds vertically instead of horizontally as shown below.
4. How many less hexagons are needed to build the term with $42$ dotted hexagons now?

Term Number	\(1\)	\(2\)	\(3\)	\(4\)
Term Value	\(22\)	\(29\)	\(36\)	\(43\)

Term Number	\(1\)	\(2\)	\(3\)	\(4\)
Term Value	\(-22\)	\(-29\)	\(-36\)	\(-43\)