Finding Next Terms: Error Analysis & Misconceptions
Mathematics
Year 9
13 questions
~26 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on identifying and correcting misconceptions when finding the next terms in arithmetic sequences. Includes error analysis, procedural practice, and real-world applications.
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Finding Next Terms: Error Analysis & Misconceptions
Subject: MathematicsGrade: Year 9
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Untitled Worksheet
Grade Year 9
A
Introduction
Review the formula for finding the next term in an arithmetic sequence: if the sequence is a, a + d, a + 2d, ..., then the next term is given by last term + common difference. Pay attention to common mistakes such as incorrect common difference or misalignment.
B
Fluency & Practice
Answer the following questions to practice calculating the next terms in various sequences.
1.
Find the next term in the sequence: 5, 8, 11, 14, ...
[2 marks]2.
Calculate the next term of: 20, 15, 10, 5, ...
[2 marks]3.
What is the next term for the sequence: 2, 4, 6, 8, ...?
[2 marks]4.
Determine the next term in: -3, 0, 3, 6, ...
[2 marks]C
Problem Solving & Reasoning
Solve these multi-step problems, explaining your reasoning.
1.
A sequence starts with 12 and increases by 3 each time. What is the 10th term? Show your working.
[3 marks]2.
The sequence 50, 45, 40, 35, ... is an arithmetic sequence. Find the 8th term and explain how you found it.
[3 marks]3.
A pattern in a sequence is described as starting at 7 and decreasing by 2 each step. Find the 15th term and justify your answer.
[3 marks]D
Real-world Applications
Apply your understanding to real-world contexts involving pattern recognition.
1.
A car starts with a full tank of 40 liters. It consumes 4 liters every hour. Write the sequence representing the remaining fuel after each hour. What is the amount of fuel after 10 hours?
[3 marks]2.
A walkathon raises $500 in the first week and increases the amount raised by $50 each subsequent week. Write the sequence and find out how much will be raised in the 12th week.
[3 marks]E
Challenge & Extension
Tackle these more difficult problems to deepen your understanding.
1.
A sequence starts with 3, and each subsequent term is obtained by adding the previous two terms (like a Fibonacci sequence). If the first term is 3 and the second term is 5, find the 8th term.
[4 marks]2.
Construct an arithmetic sequence starting at 10 with a common difference of -3. Find the 20th term and explain your reasoning.
[4 marks]F
Mixed Review & Error Analysis
Identify and correct the errors in these common misconceptions.
1.
A student states that the next term after 4, 8, 12, 16 is 20, but they added 4 instead of the common difference. Identify the mistake and correct it.
[3 marks]2.
A student writes the sequence: 2, 4, 8, 16, ... and claims it's arithmetic. Explain why this is incorrect and identify the pattern.
[3 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet