Exploring Recursive Formulas in Arithmetic Sequences

This video tutorial explains the concept of recursive formulas in arithmetic sequences. It defines a recursive formula and demonstrates how to use it to find terms in a sequence. The video provides examples with sequences 2, 5, 8, 11 and 62, 50, 38, showing how to calculate subsequent terms using the recursive formula. It also covers how to write a sequence from a given recursive formula and encourages viewers to practice on their own.

What is a recursive formula?

• A formula that defines each term of a sequence using the preceding term

• A formula that defines each term of a sequence using a random value

• A formula that defines each term of a sequence using a constant value

• A formula that defines each term of a sequence using the next term

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

• The next term

• The previous term

• The common difference

• The first term

What is the common difference in the sequence 2, 5, 8, 11?

• 8

• 2

• 3

• 5

Using the recursive formula a_n = a_(n-1) + 3, what is the fifth term if the fourth term is 11?

• 11

• 14

• 17

• 20

Using the recursive formula a_n = a_(n-1) + 3, what is the sixth term if the fifth term is 14?

• 14

• 17

• 23

• 20

What is the common difference in the sequence 62, 50, 38?

• -12

• -24

• 12

• 24

Using the recursive formula a_n = a_(n-1) - 12, what is the fourth term if the third term is 38?

• 26

• 38

• 50

• 62

Using the recursive formula a_n = a_(n-1) - 12, what is the fifth term if the fourth term is 26?

• 38

• 50

• 26

• 14

Given the first term -13 and the recursive formula a_n = a_(n-1) + 6, what is the second term?

• -19

• 5

• -1

• -7

Given the first term -13 and the recursive formula a_n = a_(n-1) + 6, what is the fifth term?

• 17

• 11

• 5

• -1