Recursive formulas for arithmetic sequences | Mathematics I | High School Math | Khan Academy

TL;DR

The video explains how to find the missing parameters in a recursive definition of an arithmetic sequence.

Transcript

• [Voiceover] g is a function that describes an arithmetic sequence. Here are the first few terms of the sequence. So let's say the first term is four, second term is 3 4/5, third term is 3 3/5, fourth term is 3 2/5. Find the values of the missing parameters A and B in the following recursive definition of the sequence. So they say the nth term is ... Read More

Key Insights

• 🍉 The value of A in a recursive definition of an arithmetic sequence is determined by the first term.
• 😃 The value of B in a recursive definition of an arithmetic sequence can be found by identifying the common difference between consecutive terms.
• 💼 The first case of the recursive definition is only applicable when n equals one.

Questions & Answers

Q: How do you find the value of A in a recursive definition of an arithmetic sequence?

A in a recursive definition of an arithmetic sequence is determined by the first term. In this case, the first term is four, so A is equal to four.

Q: How do you find the value of B in a recursive definition of an arithmetic sequence?

B in a recursive definition of an arithmetic sequence is found by identifying the common difference between consecutive terms. In this case, the common difference is -1/5, so B is equal to -1/5.

Q: Can I use the first case of the recursive definition for any value of n?

No, the first case of the recursive definition is only applicable when n equals one. For any other value of n, the second case should be used.

Q: How can I find the nth term using the recursive definition and the determined values of A and B?

To find the nth term, substitute the n-1th term into the recursive definition and subtract B (-1/5) from it. For example, if n is four, the nth term would be g of three minus 1/5.

Summary & Key Takeaways

• The video discusses finding the missing parameters A and B in a recursive definition of an arithmetic sequence.

• A is determined by the first term of the sequence, which is four.

• B is determined by finding the common difference between consecutive terms in the sequence, which is subtracting 1/5.