Learn with Amar
Teaching video
A teaching recording for this chapter has not been published yet. Start with the worked example below and explore the related animations where available.
Grade 9 chapters and video availability01 · Read and understand
What you will learn
- Derive a term formula for a fixed-ratio sequence.
- Justify the method and check its domain, units, or logical conditions.
Before you start
Signed arithmetic, fraction and decimal operations, one-step equations, and introductory coordinate graphs.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
A geometric sequence begins 3,6,12,24. Find its eighth term.
Why this math matters
Represent repeated scaling with powers rather than an additive rule. The example connects a stated condition to a conclusion and then checks whether the result satisfies that condition.
Set up the model
A useful answer starts with clear assumptions:
- Use the real-number system and the restrictions or data model stated in the question unless another domain is specified.
- Treat provided measurements as exact classroom-model values unless an approximation or uncertainty is stated.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Count repeated factors in a geometric sequence
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A geometric sequence begins 3,6,12,24. Find its eighth term.
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the conditions
First term a₁=3; common ratio r=2
Each term is twice the previous term.
Develop the calculation
aₙ=3·2ⁿ⁻¹
The nth term follows n−1 multiplications after the first.
Check and interpret
a₈=3·2⁷=384
Repeated multiplication produces exponential dependence on the index.
The result
a₈=3·2⁷=384
Repeated multiplication produces exponential dependence on the index.
Common mistakes to catch
- A fixed difference is arithmetic; a fixed ratio is geometric.
- Count multiplications from the specified first index.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
Find the fifth term of 81,27,9,… with fixed ratio.
Show a hint
Use ratio one third four times.
Reveal answer and explanation
1
81(1/3)⁴=81/81=1.
Practice 2
Can a geometric sequence alternate signs?
Show a hint
Consider a negative common ratio.
Reveal answer and explanation
Yes
Starting at two with ratio −2 gives 2,−4,8,−16,….
Take the idea with you
Represent repeated scaling with powers rather than an additive rule.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Turn repeated percentage growth into a multiplier
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