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

[table][br][tr][br] [td][b]Factual Inquiry Questions[/b][br] [list][br] [*]What is the formula for the nth term of an arithmetic sequence?[br] [*]How is the sum of the first n terms of an arithmetic series calculated?[br] [/list][br] [/td][br] [td][b]Conceptual Inquiry Questions[/b][br] [list][br] [*]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?[br] [*]How can understanding arithmetic sequences and series aid in solving real-world problems, such as planning finances or scheduling tasks?[br] [/list][br] [/td][br] [td][b]Debatable Inquiry Questions[/b][br] [list][br] [*]Is the study of arithmetic sequences and series more applicable to everyday life than that of geometric sequences and series? Why or why not?[br] [*]Can the principles of arithmetic sequences and series be effectively used to understand patterns in nature and society?[br] [/list][br] [/td][br][/tr][br][/table][br]

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

Watch the two videos below before attempting the questions

Alternatively these videos are very short, and work through exam-style questions directly.[br][br] Arithmetic sequences 1 [url=https://youtu.be/jJCRJ1XOq9s]https://youtu.be/jJCRJ1XOq9s[/url]  Arithmetic sequences 2 [url=https://youtu.be/Q9jTuF6KX6k]https://youtu.be/Q9jTuF6KX6k[/url]  Arithmetic sequences 3 [url=https://youtu.be/hZN9VGVSygQ]https://youtu.be/hZN9VGVSygQ[/url] [br]

Testing your understanding with exam-style questions