Determine whether the following patterns are increasing, decreasing or neither:
7, 6, 11, 3, 9
25, 22, 19, 16, 13
6.5, 6.6, 6.7, 6.8, 6.9
5, 4, 9, 1, 7
21, 20, 19, 18, 17
5.4, 9.4, 6.2, 6.6, 7.0
For each of the following patterns:
State whether the pattern is increasing or decreasing.
Determine by how much the pattern is increasing or decreasing each time.
9.5, 9.7, 9.9, 10.1, 10.3
15.3, 14.7, 14.1, 13.5, 12.9
31, 25, 19, 13
15, 21, 27, 33
5, 12, 19, 26
34, 28, 22, 16
17, 23, 29, 35
9, 16, 23, 30
Find the next number in the following sequences:
2,4, 6, 8
7, 9, 11, 13
65, 58, 51, 44
2,\, 2\dfrac{1}{2},\, 3,\, 3\dfrac{1}{2}
1,\, 1\dfrac{1}{3},\, 1\dfrac{2}{3},\, 2
Determine whether each sequence is finite or infinite:
1, 2, 3, 4, 5, 6
-1, -2, -3, -4, -5, -6\text{, . . .}
-1, -2, -3, -4, -5
1, 2, 3, 4, 5, 6\text{, . . .}
If all the dates in July were used to form a sequence, would the sequence be finite or infinite?
If all the years from 1966 onwards were used to form a sequence, would the sequence be finite or infinite?
Consider the rule: "The starting number, N, is doubled, then 4 is subtracted to get the answer A."
Use the rule to complete the table of values:
| \text{Starting Number }(N) | 12 | 13 | 14 | 15 |
|---|---|---|---|---|
| \text{Answer }(A) |
Write the rule for A in terms of N.
Consider the rule: "The starting number, N, has 9 added to it. The sum is then multiplied by 5 to get the answer A."
Use the rule to complete the table of values:
| \text{Starting Number }(N) | 4 | 5 | 6 | 7 |
|---|---|---|---|---|
| \text{Answer }(A) |
Write the rule for A in terms of N.
Each of the patterns below was created in steps using matchsticks.
Complete the following table of values for each of the given patterns:
| \text{Step number} \left(t\right) | 1 | 2 | 3 | 4 | 5 | 10 |
|---|---|---|---|---|---|---|
| \text{Number of matchsticks}\left(m\right) |
Write a formula that describes the relationship between the number of matches, m, and the step number, t.
Vanessa is making a sequence of shapes out of tiles. She creates a table comparing the sequence number of a shape to the number of tiles needed to make it:
| \text{Sequence} \\ \text{number } \left(n\right) | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| \text{Number of} \\ \text{tiles } \left(T\right) | 3 | 5 | 7 |
How many new tiles are added at each step?
Find how many tiles Vanessa will need to make the next three shapes in the sequence by completing the table of values.
An equation to represent the relationship between a shape's sequence number and the number of tiles needed can be written in the form T=s+(n-1)d, where s is the starting number of tiles and d is the number of new tiles added each step.
Find how many tiles Vanessa will need to make the 20th shape in the sequence.