Formula: Problem Solving & Reasoning
Mathematics
Grade 7
14 questions
~28 mins
1 views0 downloads
About This Worksheet
This worksheet focuses on understanding and applying the formula for geometric sequences. It guides students through procedural mastery, problem-solving, real-world applications, and extension challenges.
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Formula: Problem Solving & Reasoning
Subject: MathematicsGrade: Grade 7
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Untitled Worksheet
Grade Grade 7
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Write the formula for the nth term of a geometric sequence.
[2 marks]2.
Calculate the 5th term of a geometric sequence where the first term is 3 and the common ratio is 2.
[3 marks]3.
If the first term of a sequence is 5 and the 4th term is 40, find the common ratio.
[3 marks]4.
Construct the first three terms of a geometric sequence with a_1 = 4 and r = 3.
[3 marks]B
Problem Solving & Reasoning
Solve the following multi-step problems. Show detailed working in the grid.
1.
A bacteria culture starts with 2 bacteria. Each hour, the bacteria multiply by a factor of 3. How many bacteria will there be after 4 hours?
[4 marks]2.
The sixth term of a geometric sequence is 96, and the first term is 3. Find the common ratio and verify the 3rd term.
[4 marks]3.
A savings account increases by 5% annually, starting with $200. What is the amount after 3 years? (Round to two decimal places.)
[4 marks]C
Real-world Applications
Apply your understanding to real-life scenarios.
1.
A plant doubles in height every month. If it is 10 cm tall at the start, how tall will it be after 6 months?
[3 marks]2.
A car's value depreciates by 10% each year. If the car originally cost $15,000, what is its value after 4 years?
[3 marks]D
Challenge & Extension
Attempt these more difficult problems to extend your understanding.
1.
The 3rd term of a geometric sequence is 18, and the 6th term is 72. Find the first term and the common ratio.
[4 marks]2.
A population of 100 bacteria triples every hour. Write the formula for the population after n hours and calculate the population after 8 hours.
[4 marks]E
Mixed Review
Solve these questions to review different aspects of the formula.
1.
What is the 10th term of a geometric sequence with a_1=1 and r=4?
[3 marks]2.
Construct a sequence with first term 5 and common ratio 1/2. Write the first four terms.
[3 marks]F
Error Analysis
Identify and correct the common mistake in the following problem.
1.
A student calculates the 4th term of a sequence using the formula a_4= a_1 + 3r. Is this correct? Explain and correct if needed.
[4 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet