Download picture patterns

Notes
PICTURE AND NUMBER PATTERNS
Complete the following picture patterns by finding the next term(s).
1.





2.
___
______
_________
3.
___
______
_________

_____
5.
______
_________
_____
_____________
50th shape
100th shape
_____________
_____________
___________
_____________
50th shape
100th shape
_____________
_____________
___________
4.
___
_____
_______
___________
50th shape
100th shape
___________
___________
___________






_____________
50th shape
100th shape
___
______
_________
_____________
_____________
___________
6. Underneath the picture patterns in # 2, 3, 4, and, 5 write a corresponding number pattern.
7. Find the number underneath the 50th and 100th shape for # 2, 3, 4, and 5.
8. Complete the following number patterns by finding the missing terms.
a.
5, 7, 9, 11, 13, 15, 17, __________, _________, __________
b.
-4, -9, -14, -19, -24, -29, -34, __________, _________, __________
c.
405, 135, 45, 15, __________, _________, __________
d.
5, 6, 8, 11, __________, _________, __________, 33, __________, 50, __________
e.
2, 6, 18, 54, ________, __________, 1458, __________
f.
2, 3, 5, 8, 13, 21, __________, _________, __________, 144, __________
g.
3, 9, 27, 81, __________, __________, 2187, ___________, __________
Underneath each number patterns above write if the sequence is arithmetic, geometric or neither.
Arithmetic Sequence = a sequence where you add or subtract the same number to get the next term.
Geometric Sequence = a sequence where you multiply or divide by the same number to get the next term.
Neither = all the other sequences!
©Dr Barbara Boschmans
Page 1 of 4
Notes
9. Use the rule to determine the first eight terms of each sequence.
Example: Each term is the term number times 3 plus 2.
First Term
1×3+2
5
Second Term
2×3+2
8
Third Term
3×3+2
11
Fourth Term
4×3+2
14
Fifth Term
5×3+2
17
Etc.
a) Each term is the term number times 4 plus 1.
1
2
3
4
5
6
7
8
___
___
13
___
___
___
___
33
b) Each term is the term number times 6 minus 3.
1
2
3
4
5
6
7
8
___
___
___
___
27
___
___
___
c) Each term is the term number times – 4 plus 50.
1
2
3
4
5
6
7
8
46
___
___
___
___
___
___
___
d) Each term is the term number squared plus 3.
1
2
3
4
5
6
7
8
___
___
___
___
___
39
___
___
e) Each term is the term number times the next term number.
1
2
3
4
5
6
7
8
___
___
___
20
___
___
___
___
f)
Find the differences between the successive terms in #1-3. What do you notice? What do we call this
type of sequence?
g) If you did not know the rules for the sequences in # 4-5, how could you find the next five terms of each
sequence?
10. Let’s use this example:
5, 8, 11, 14, 17, …
Organizing this information in a table will be useful:
Term
Number
1
2
3
4
5
Term
5
8
11
14
17


Difference
___
___
What is the constant difference? ______
©Dr Barbara Boschmans
6
7
8





___
___
___
___
___
Page 2 of 4
Notes
You need to find a general equation for this sequence (also called the “nth” term) and use it to find the 100th
term. Let’s help you out:
Term Number
Constant Difference
What Was Done?
To Get
1

3

3
_____
=
5
1st Term
2

3

6
_____
=
8
2nd Term
3

3

_____
_____
=
11
3rd Term
4

___

_____
_____
=
14
4th Term
5

___

_____
_____
=
17
5th Term
n

___

_____
_____
=
_______
nth Term
100

___

_____
_____
=
_______
100th Term
General Equation / nth term / rule: ____________
100th Term: ________
Find the rule/nth term for each of the following sequences and use your rule to find the 25th and 100th term.
nth Term
25th Term
100th Term
a. 9, 14, 19, 24, 29, ___, ___, ___, …,
__________
__________
_________
b. -3, 4, 11, 18, 25, ___, ___, ___, …,
__________
__________
_________
c. -1, -4, -7, -10, -13, ___, ___, ___, …,
__________
__________
_________
d. 104, 102, 100, 98, 96, ___, ___, ___, …,
__________
__________
_________
11. Find the sum for each of the following arithmetic sequences.
a. 9, 14, 19, 24, 29, … , 499, 504
Sum = 9 + 14 + 19 + … + 499 + 504 = ______________________
b. -3, 4, 11, 18, 25, … , 683, 690
Sum = -3 + 4 + 11 + … + 683 + 690 = ______________________
c. -1, -4, -7, -10, -13, … , -295, -298
Sum = -1 + -4 + -7 + … + -295 + -298 = _____________________
d. 104, 102, 100, 98, 96, … , -92, -94
Sum = 104 + 102 + 100 + … + -92 + -94 = _________
©Dr Barbara Boschmans
Page 3 of 4
Notes
12. Let’s use this example:
2, 6, 18, 54, 162, …
Organizing this information in a table will be useful:
Term
Number
1
2
3
4
5
Term
2
6
18
54
162




6

7
8


Factor
___
___
___
___
___
___
___
What is the factor? ______
You need to find a general equation for this sequence (also called the “nth” term) and use it to find the 100th
term. Let’s help you out. This time we will start with our numbers in the sequence and “peel” them apart.
Sequence
Number
First Term Factored
Out
Re-write using the
Factor
Term
Number
Term Number
Minus One
2
=2
= 2 x 30
1
0
1st Term
6
=2x3
= 2 x 31
2
1
2nd Term
18
=2x9
= 2 x 32
3
2
3rd Term
54
= 2 x 27
= 2 x 33
4
3
4th Term
162
= 2 x 81
= 2 x 34
5
4
5th Term
_______
_______________
n
n-1
nth Term
_______
_______________
100
99
100th
Term
=
=
General Equation / nth term / rule: ____________
100th Term: ________
Find the rule/nth term for each of the following sequences and use your rule to find the 25th and 100th term.
nth Term
25th Term
100th Term
a. 400, 200, 100, 50, 25, ___, ___, ___, …,
__________
__________
_________
b. -1, -5, -25, -125, -625, ___, ___, ___, …,
__________
__________
_________
c. 4, 8, 16, 32, 64, ___, ___, ___, …,
__________
__________
_________
d. 64, -32, 16, -8, 4, ___, ___, ___, …,
__________
__________
_________
©Dr Barbara Boschmans
Page 4 of 4