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Teaching video
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Grade 11 chapters and video availability01 · Read and understand
What you will learn
- Derive a finite geometric-sum formula by subtraction.
- Justify the conclusion "S=(243−1)/2=121" using the stated assumptions.
Before you start
Exponents and algebraic rearrangement.
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
Find S=1+3+3²+3³+3⁴.
Why this math matters
Derive a finite geometric-sum formula by subtraction. This worked micro-lesson connects a precise mathematical condition to a conclusion you can check. The transfer task asks you to change the setting and decide which parts of the reasoning still apply.
Set up the model
A useful answer starts with clear assumptions:
- There are exactly five displayed terms.
- The common ratio is three.
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.
Add repeated multiplicative contributions efficiently
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Find S=1+3+3²+3³+3⁴.
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.
Build the model
3S=3+3²+3³+3⁴+3⁵
Multiplying shifts each contribution by one position.
Work through the mathematics
3S−S=3⁵−1
All shared interior terms cancel.
Check the conclusion
S=(243−1)/2=121
The formula handles a total of five terms, not just the final term.
The result
S=(243−1)/2=121
The formula handles a total of five terms, not just the final term.
Common mistakes to catch
- The term count and final exponent differ by one here.
- The ratio-one case needs its own formula.
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 2+6+18+54.
Show a hint
Factor out two and sum four powers of three.
Reveal answer and explanation
80
2(3⁴−1)/(3−1)=80.
Practice 2
What if the common ratio equals one?
Show a hint
The division formula has zero denominator.
Reveal answer and explanation
Add n identical terms directly
The sum is n times the first term.
Take the idea with you
Compute the total contribution of a finite sequence of scaled layers.
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: Select one coefficient without expanding every term
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