1. Fill in the blanks.
a) 156, (?), 217
b) 3, 15, (?), 63
c) (?), 27, 30, 33, 36
d) 1, 5, 13, 25, (?), 61
e) (?), 14, 18, 22, 26
*a) 156, 187, 217
b) 3, 15, 39, 63
c) 24, 27, 30, 33, 36
d) 1, 5, 13, 25, 41, 61
e) 10, 14, 18, 22, 26*
2. Find the odd term out in each group.
a) 2, 4, 8, 10, 16
b) 1, 2, 5, 10, 21
c) 1, 4, 9, 16, 28
d) 2, 5, 14, 26, 42
e) 2, 6, 18, 34, 62
*a) 10
b) 5
c) 28
d) 42
e) 6*
3. What is the next term in each sequence?
a) 2, 4, 8, 16, ___
b) 3, 5, 7, 9, ___
c) 2, 4, 6, 8, ___
d) 1, 1, 2, 3, ___
e) 1, 4, 9, 16, ___
*a) 32
b) 11
c) 10
d) 5
e) 25*
4. Find the missing term.
a) _, 2, 4, 6, 8
b) 3, 5, _, 9, 11
c) 1, 4, 9, _, 16
d) 2, 5, 10, _, 20
e) 2, 6, 18, _, 62
*a) 0
b) 7
c) 13
d) 15
e) 34*
5. Write the next three terms of each pattern.
a) 1, 4, 9, 16
b) 3, 6, 11, 18
c) 1, 2, 4, 8
d) 2, 4, 7, 11
e) 2, 5, 10, 17
*a) 25, 36, 49
b) 27, 38, 51
c) 16, 32, 64
d) 16, 22, 29
e) 26, 37, 50*
6. Simplify the following patterns:
a) 12 + 3, 15 + 3, 18 + 3
b) 20 - 5, 15 - 5, 10 - 5
c) 10 x 2, 20 x 2, 30 x 2
d) 15 ÷ 3, 12 ÷ 3, 9 ÷ 3
e) 25 + 10, 25 + 20, 25 + 30
*a) 12 + 3n
b) 20 - 5n
c) 10 x 2n
d) 15 ÷ 3n
e) 25 + 10n*
7. Find the rule for each pattern.
a) 2, 4, 6, 8
b) 1, 4, 9, 16
c) 2, 5, 10, 17
d) 3, 8, 15, 24
e) 1, 3, 6, 10
*a) Add 2 to the previous number.
b) Square numbers (numbers multiplied by themselves).
c) Add 3 to the cube of the previous number.
d) Add 7 to twice the previous number.
e) Add 2 to the triangular number of the previous term.*
8. Create your own pattern and then write the rule for it.
*Pattern:* 1, 3, 6, 10, 15, 21
*Rule:* Add the next odd number (3, 4, 5, 6, 7, 8) to the previous number to obtain the next term.
9. Identify the following patterns.
a) 2, 4, 8, 16, 32
b) 1, 3, 6, 10, 15
c) 1, 2, 4, 7, 11
d) 5, 10, 20, 40, 80
e) 1, 2, 6, 24, 120
*a) Powers of 2
b) Triangular numbers
c) Prime numbers
d) Numbers that double
e) Factorials*
10. Write a short story about patterns in the world around us.
"In a small town surrounded by rolling hills, a young girl named Emily noticed something peculiar while walking home from school one day. She observed a pattern of pebbles arranged in a certain way along the path. She continued her walk, spotting patterns everywhere - in the arrangement of leaves on trees, the waves crashing the shores, and the colors of the flowers blooming in the fields.
Curious about these patterns, Emily decided to explore further. She began investigating the patterns found in music, the architecture of buildings, and even human behaviors. She discovered that understanding these patterns could unravel the mysteries of the world around her.
With each new pattern she encountered, Emily's fascination grew, leading her on an exciting journey of exploration and discovery. She realized that patterns were like hidden treasures, and unlocking them could lead to a better understanding of the universe and our place in it."