Exploring Recursive Forms in Arithmetic Sequences

The video tutorial explains recursive formulas, detailing how to determine the first term and the common difference to find subsequent terms. It provides examples with both negative and positive common differences, demonstrating how to apply the formula. The tutorial also covers writing recursive forms from given sequences, emphasizing the importance of identifying the first term and the common difference.

What does the recursive formula specify?

• The last term and how to find the next term

• The first term and how to find each subsequent term

• The common ratio and the first term

• The sum of all terms

In the formula a_n = a_(n-1) + d, what does 'd' represent?

• The first term

• The common ratio

• The common difference

• The last term

If the first term is 4 and the common difference is -3, what is the second term?

• 1

• -1

• 7

• 0

Given the sequence starting with 4 and a common difference of -3, what is the third term?

• 0

• 1

• -5

• -2

If the first term is 9 and the common difference is +4, what is the second term?

• 12

• 17

• 13

• 5

For the sequence starting with 9 and a common difference of +4, what is the fourth term?

• 25

• 13

• 17

• 21

What should you do after trying the next two examples?

• Submit your work

• Check your work

• Ask for help

• Move to the next chapter

Given the sequence 12, 8, 4, what is the common difference?

• 4

• -8

• -4

• 8

For the sequence 13, 18, 23, 28, what is the recursive formula?

• a_n = a_(n-1) + 4

• a_n = a_(n-1) - 4

• a_n = a_(n-1) + 5

• a_n = a_(n-1) - 5

What is the first term in the sequence 13, 18, 23, 28?

• 13

• 18

• 23

• 28