1.1: Describing Patterns
Alan puts $15 more in savings each month. In the first month of savings, he put in $30. Create a table to show how much is in his savings and say how much he has after 5 months of savings.
Table I check. $75
The common difference of a sequence is 3. It's third term is 7. What is it's fifth term?
13
An arithmetic sequence is the following.
2, 5, 8, 11... with 2 being the first term. Will the 20th term be odd or even?
Odd, all the odd terms are even and all the even terms are odd.
Distribute 5(3x-4)
15x-20
Evaluate 5k2+10 for k=3
55
Is the following sequence arithmetic? Show why/why not.
3, 5, 8, 12, 17...
No, no consistent common difference
A bus travels 1 mile south each time it goes 3 miles east. If it has traveled 5 miles south, how many miles east has it traveled?
15 miles east
Simplify: 3x-7y+10x-4
13x-7y-4
A shop is selling shoes where each pair is the same price. They have a sale if you buy more than one. Let C=20+13(n-1) where C is the cost in dollars and n is how many shirts you buy.
1) How much did the first shirt cost?
2) How much will each other shirt cost?
First shirt was $20. Each additional will be $13.
The third term of an arithmetic sequence is 8 and the 6th term is 2. What is the common difference and what is the first term?
Common difference is -2 and the first term is 12
A pattern will go ABCABCABCABC.... forever. What is the 120th letter of the pattern?
C
-4x+10
A pool of 75 people are being split into teams. P people do not show up and then the remaining are split into 3 teams. Write a rule that represents how many people will be on each team in terms of P
(75-x)/3
The first term of an arithmetic sequence is 8 and the common difference is 3. Write a rule for the value (v) of the sequence on step n.
v=5+3n
8 people are at the movies. If you lock in the two people sitting on the left, how many ways are there to arrange the other 6 people?
720 ways! 1x2x3x4x5x6
The legs of a right triangle are 6 and 8 inches. How long is the hypotenuse?
10 inches
3 children and 4 adults need to get across a river. Children are half the weight of adults. Only one adult can be carried by the boat for each trip. How many trips would it take to get across the river? Each single crossing counts as 1
19 trips
The third term of an arithmetic sequence is 5. The 15th term is -31. Write a rule for the value (v) of the sequence on term n.
v=-3n+14
7 postcards and 5 stickers can be purchased by Devon but they ran out of all their money. They also could have purchased 8 postcards and 2 stickers and run out of money.
They come back another day and can afford 12 postcards if they only purchased postcards. How many stickers could they buy if they only purchased stickers?
36 stickers
There are three boxes with messages on them. One box has a prize. Only one of the box's messages is true. The other two boxes are lying.
The first box has "the prize is in this box"
The second box has "the prize is not in this box"
The third box has "the prize is not in box 1"
Which box has the prize?
Box 2:
If it was in box 1, both 1 and 2 would be true statements.
If it was in box 3, both 2 and 3 would be true statements.