Students analyze complex sequences and multi-step pattern rules. Part A has four multiple-choice questions about a doubling-plus-one pattern, a multiply-by-3 input-output table, and a halving sequence. Part B has five fill-in-the-blank problems including a multiply-by-3 geometric sequence reaching 162, a subtract-7 function table, and an addition-table extension.
Identifying the rule in sequences with non-constant differences marks a significant leap in algebraic thinking.
Style:
Patterns and Number Sequences
Part A: Multiple Choice
Circle the best answer for each question.
1. In the pattern 1, 3, 7, 15, what is the rule?
A) Add 2 each time
B) Double and add 1
C) Multiply by 3
D) Add 4 each time
2. An input-output table uses multiply by 3. Which input gives an output of 27?
A) 6
B) 8
C) 9
D) 7
3. What comes next in the pattern 64, 32, 16, 8?
A) 6
B) 2
C) 4
D) 0
4. In the pattern 5, 10, 15, 20, 25, 30, what is the 8th number?
A) 35
B) 45
C) 40
D) 50
Part B: Fill in the Blank
Write the correct answer on each line.
1. In the pattern 2, 6, 18, 54, each number is multiplied by 3. The next number is 162.
2. If the rule is subtract 7 and the input is 50, the output is 43.
3. In the addition table, the row for 8 shows 8, 16, 24, 32. The next number is 40.
4. The pattern 100, 85, 70, 55, 40 follows the rule subtract 15.
5. In the pattern 4, 12, 36, 108, the missing number is 36.
Patterns and Number Sequences
★ Part A: Multiple Choice
Circle the best answer for each question.
1. In the pattern 1, 3, 7, 15, what is the rule?
A) Add 2 each time
B) Double and add 1
C) Multiply by 3
D) Add 4 each time
2. An input-output table uses multiply by 3. Which input gives an output of 27?
A) 6
B) 8
C) 9
D) 7
3. What comes next in the pattern 64, 32, 16, 8?
A) 6
B) 2
C) 4
D) 0
4. In the pattern 5, 10, 15, 20, 25, 30, what is the 8th number?
A) 35
B) 45
C) 40
D) 50
★ Part B: Fill in the Blank
Write the correct answer on each line.
1) In the pattern 2, 6, 18, 54, each number is multiplied by 3. The next number is 162.
2) If the rule is subtract 7 and the input is 50, the output is 43.
3) In the addition table, the row for 8 shows 8, 16, 24, 32. The next number is 40.
4) The pattern 100, 85, 70, 55, 40 follows the rule subtract 15.
5) In the pattern 4, 12, 36, 108, the missing number is 36.
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12-18 minutes
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