GeoGebra Classroom

# Arithmetic (AA/AI SL 1.2)

## Keywords

Arithmetic Sequences等差数列（とうさすうれつ）等差数列（děng chā shù liè）등차 수열 (deungcha suyeol)
Arithmetic Series等差シリーズ（とうさシリーズ）等差级数（děng chā jí shù）등차 시리즈 (deungcha sirijeu)
nth term formulan番目の項の公式（nばんめのこうのこうしき）第n项公式（dì n xiàng gōng shì）n번째 항의 공식 (nbeonjjae hang-ui gongsik)
Sum of the first n terms初項からn項までの和（しょこうからnこうまでのわ）前n项和（qián n xiàng hé）첫 n 항의 합 (cheot n hang-ui hap)
Common difference公差（こうさ）公差（gōng chā）공차 (gongcha)

## Inqury questions

 Factual Inquiry Questions What is the formula for the nth term of an arithmetic sequence? How is the sum of the first n terms of an arithmetic series calculated? Conceptual Inquiry Questions Why does the formula for the sum of an arithmetic series involve multiplying the average of the first and last terms by the number of terms? How can understanding arithmetic sequences and series aid in solving real-world problems, such as planning finances or scheduling tasks? Debatable Inquiry Questions Is the study of arithmetic sequences and series more applicable to everyday life than that of geometric sequences and series? Why or why not? Can the principles of arithmetic sequences and series be effectively used to understand patterns in nature and society?

Exploration Title: "The Arithmetic Adventure" Objective: Embark on an arithmetic adventure to discover the hidden treasures of sequences and series. Use the powers of addition and difference to navigate through the world of arithmetic progression. Mission Steps: 1. Term Treasure Hunt: - Calculate the 100th term of the sequence that begins with 5 and has a common difference of 7. - Compare the 100th term with the 1st term and discuss how quickly the terms grow. 2. Sum Saga: - Find the sum of the first 50 terms of the sequence you investigated in step 1. - How does this sum relate to the individual terms of the sequence? 3. Common Difference Challenge: - Change the common difference to -3. What happens to the sequence? - How does a negative common difference affect the sum of the series? Questions for Investigation: 1. Patterns of Progression: - Why does an arithmetic series with a positive common difference grow without bound? 2. Sum vs. Term: - How does the sum of the terms compare to the value of the last term in a long arithmetic sequence? 3. Practical Applications: - Where do you encounter arithmetic sequences in real life? (Think savings plans, paying off debt, etc.) Engagement Activities: - "Sequence Prediction": Without calculation, predict whether the 200th term will be an even or odd number for a given first term and common difference. - "Sum Duel": Compete with a partner to see who can calculate the sum of the first 'n' terms of a sequence faster. Dive into this arithmetic expedition, uncover the linear patterns of sequences, and unveil the accumulating power of series. Happy calculating!

## Part 2 - Checking understanding

Watch the two videos below before attempting the questions
Alternatively these videos are very short, and work through exam-style questions directly.  Arithmetic sequences 1 https://youtu.be/jJCRJ1XOq9s  Arithmetic sequences 2 https://youtu.be/Q9jTuF6KX6k  Arithmetic sequences 3 https://youtu.be/hZN9VGVSygQ

What is the common difference of the arithmetic sequence 4, 7, 10, 13, ...?

Select all that apply
• A
• B
• C
• D

Given the first term of an arithmetic sequence is 5 and the common difference is 3, what is the 10th term?

Select all that apply
• A
• B
• C
• D

## The 3rd term of an arithmetic sequence is 9 and the 8th term is 24. What is the first term?

Select all that apply
• A
• B
• C
• D

If the sum of the first n terms of an arithmetic sequence is given by what is the common difference?

Select all that apply
• A
• B
• C
• D

## Part 3 - Testing your understanding with exam-style questions

Testing your understanding with exam-style questions