Geometric (AA/AI SL 1.3)
Keywords
| English | Japanese | Korean | Chinese Simplified |
| Geometric Sequence | 等比数列 | 등비 수열 | 等比数列 |
| nth Term | n番目の項 | n번째 항 | 第n项 |
| Geometric Series | 等比級数 | 등비 급수 | 等比级数 |
| Sum of the First n Terms | 最初のn項の和 | 첫 n 항의 합 | 前n项和 |
| Convergence | 収束 | 수렴 | 收敛 |
| Divergence | 発散 | 발산 | 发散 |
| Exponential Growth | 指数関数的成長 | 지수 성장 | 指数增长 |
| Exponential Decay | 指数関数的減少 | 지수 감소 | 指数衰减 |
| Common Ratio | 公比 | 공비 | 公比 |
| Sigma Notation | シグマ記法 | 시그마 표기법 | Σ表示法 |
| Sum to Infinity | 無限大への和 | 무한대까지의 합 | 无穷级数的和 |
Inquiry questions
Factual Inquiry Questions
| Conceptual Inquiry Questions
| Debatable Inquiry Questions
|
The Great Geometric Quest
Exploration Title: The Great Geometric Quest
Objective:
Embark on a quest to unlock the secrets of geometric sequences and series. Use the given applet to uncover the hidden patterns and sum up your findings!
Mission Steps:
1. Sequence Sleuth:
- Find the 10th term in the sequence with a first term of 3 and a common ratio of 2.
- Predict what the 100th term might be and discuss the practicality of its magnitude.
2. Sum Search:
- Calculate the sum of the first 10 terms of the geometric sequence from step 1.
- Hypothesize about the sum of the first 100 terms. How does it compare to the 100th term alone?
3. Ratio Riddle:
- For the geometric sequence 5, 10, 20, ..., deduce the common ratio without using the applet.
- Calculate the 15th term and the sum of the first 15 terms manually, then check with the applet.
Questions for Investigation:
1. Real-life Relevance:
- How can understanding geometric sequences help in real-life scenarios like finance (interest rates) or computer science (data storage)?
2. Series Saturation:
- Is there a limit to the sum of a geometric series? Experiment with different ratios (less than 1, equal to 1, greater than 1) to find out.
3. Pattern Pursuit:
- Can you create a geometric sequence that alternates between positive and negative without changing the common ratio?
Engagement Activities:
- "Sequence Scramble": Given the 5th and 9th terms of a geometric sequence, work backward to find the first term and common ratio.
- "Sum Sprint": Challenge each other to find the sum of the first 'n' terms of a given sequence as fast as possible.
Through this investigation, become the master of multiplication patterns and understand how simple ratios build complex sequences and staggering sums.
Part 2 - Checking understanding
Watch through these two videos before attempting the questions
Alternatively, if you feel confident with the theory, watch these brief videos with worked examples of exam-style questions.
Geometric sequences 1 https://youtu.be/JwNdNSgq4uI Geometric sequences 2 https://youtu.be/_f1k58Hyy1c Geometric sequences - Harder https://youtu.be/2uEVctIHihg Geometric sequences - Sum to infinity https://youtu.be/Jpm1F9ifMRg Geometric sequences - Sum to infinity past paper question https://youtu.be/YAR_epDxhec Sigma notation https://youtu.be/tIkJNLWAbJs
If the first term of a geometric sequence is 3 and the common ratio is 4, what is the 4th term?
If the first term is 95, and the third term is 380. Find the sum to 5th term.
Part 3 - Testing understanding with exam style questions
Testing understanding with exam style questions
![[MAA 1.4] GEOMETRIC SEQUENCES.pdf](https://stage.geogebra.org/resource/dexrpkhp/cPp2EgTDNiKkiLol/material-dexrpkhp-thumb.png)
![[MAA 1.4] GEOMETRIC SEQUENCES_solutions.pdf](https://stage.geogebra.org/resource/dszn597x/Zw30d4zxyFpaFbbv/material-dszn597x-thumb.png)
