Problem Analysis and Solution
The task involves identifying patterns in sequences of numbers and determining the rule that governs each sequence. Let's solve each part step by step.
---
####
Part A: Determine the rule for each pattern
1.
Sequence: 9, 16, 23, 30
-
Step 1: Find the difference between consecutive terms:
\[
16 - 9 = 7, \quad 23 - 16 = 7, \quad 30 - 23 = 7
\]
-
Step 2: The difference is consistently 7.
-
Conclusion: The rule is to
Add 7.
-
Answer: (c) Add 7
2.
Sequence: 6, 12, 24, 48, 96
-
Step 1: Find the ratio between consecutive terms:
\[
\frac{12}{6} = 2, \quad \frac{24}{12} = 2, \quad \frac{48}{24} = 2, \quad \frac{96}{48} = 2
\]
-
Step 2: The ratio is consistently 2.
-
Conclusion: The rule is to
Multiply 2.
-
Answer: (b) Multiply 2
3.
Sequence: 243, 81, 27, 9
-
Step 1: Find the ratio between consecutive terms:
\[
\frac{81}{243} = \frac{1}{3}, \quad \frac{27}{81} = \frac{1}{3}, \quad \frac{9}{27} = \frac{1}{3}
\]
-
Step 2: The ratio is consistently \(\frac{1}{3}\), which means dividing by 3.
-
Conclusion: The rule is to
Divide 3.
-
Answer: (b) Divide 3
4.
Sequence: 6, 30, 150, 750
-
Step 1: Find the ratio between consecutive terms:
\[
\frac{30}{6} = 5, \quad \frac{150}{30} = 5, \quad \frac{750}{150} = 5
\]
-
Step 2: The ratio is consistently 5.
-
Conclusion: The rule is to
Multiply 5.
-
Answer: (d) Multiply 5
---
####
Part B: Determine the rule and complete the pattern
5.
Sequence: 36, 32, 28, 24, ________, ________
-
Step 1: Find the difference between consecutive terms:
\[
32 - 36 = -4, \quad 28 - 32 = -4, \quad 24 - 28 = -4
\]
-
Step 2: The difference is consistently \(-4\).
-
Conclusion: The rule is to
Subtract 4.
-
Step 3: Apply the rule to find the next two terms:
\[
24 - 4 = 20, \quad 20 - 4 = 16
\]
-
Answer: (d) Subtract 4, and the completed sequence is \(36, 32, 28, 24, 20, 16\).
---
Final Answers
1. (c) Add 7
2. (b) Multiply 2
3. (b) Divide 3
4. (d) Multiply 5
5. (d) Subtract 4, and the completed sequence is \(36, 32, 28, 24, 20, 16\).
\[
\boxed{(c), (b), (b), (d), (d)}
\]
Parent Tip: Review the logic above to help your child master the concept of sequences worksheet grade 6.
