Arithmetic Sequences and Recursive Rules

The video tutorial explains how to write a recursive rule for an arithmetic sequence using the example numbers 5, 7, 9, and 11. It begins by labeling the sequence positions and identifying the starting value. The tutorial then defines the recursive rule by adding a constant value to the previous term. Finally, it guides viewers to identify the correct answer choice that matches the defined recursive rule.

What is the purpose of writing a recursive rule for an arithmetic sequence?

• To determine the common difference between terms

• To find the sum of all terms in the sequence

• To calculate the product of all terms

• To express each term based on its position

In the sequence 5, 7, 9, 11, what is the position of the number 9?

• Fourth

• Second

• First

• Third

What is the starting value of the sequence discussed in the video?

• 11

• 9

• 5

• 7

How do you find the next term in an arithmetic sequence?

• Multiply the previous term by 2

• Subtract 2 from the previous term

• Add 2 to the previous term

• Divide the previous term by 2

What is the recursive rule for the sequence starting with 5 and having a common difference of 2?

• a_n = a_(n-1) - 2

• a_n = a_(n-1) + 2

• a_n = a_(n-1) + 3

• a_n = a_(n-1) * 2

Which answer choice correctly represents the recursive rule for the sequence?

• a_n = a_(n-1) + 3, a_1 = 5

• a_n = a_(n-1) + 2, a_1 = 7

• a_n = a_(n-1) + 1, a_1 = 5

• a_n = a_(n-1) + 2, a_1 = 5