Exploring Recursive Formulas in Arithmetic Sequences

This video tutorial introduces arithmetic sequences, explaining how to identify them by finding a common difference between terms. It provides examples of both arithmetic and non-arithmetic sequences, demonstrating how to determine if a sequence is arithmetic. The video also covers writing recursive formulas for arithmetic sequences, using examples to illustrate the process.

What defines an arithmetic sequence?

• Each term increases by a multiplication factor.

• The difference between consecutive terms varies.

• Each term is the square of the previous term.

• The difference between consecutive terms is constant.

Which of the following is a characteristic of an arithmetic sequence?

• The terms are subtracted by a variable difference.

• The terms are added by a constant difference.

• The terms are divided by a constant.

• The terms are multiplied by a constant.

What is the common difference in the sequence 3, 8, 13, 18?

• 10

• 15

• 5

• 3

In the sequence 3, 8, 13, 18, what operation is performed to get from one term to the next?

• Division by 5

• Multiplication by 5

• Addition of 5

• Subtraction of 5

Which sequence is not arithmetic?

• 7, 11, 15, 19

• 10, 4, -2, -8

• 6, 9, 13, 18

• 91, 84, 77, 70

What does a recursive formula for an arithmetic sequence typically include?

• The product of the previous term and the common difference.

• The sum of all previous terms.

• The next term and the common difference.

• The previous term and the common difference.

What is the fifth term in the sequence defined by the recursive formula a_n = a_(n-1) + 4, where a_1 = 7?

• 19

• 31

• 23

• 27

What is the common difference in the sequence 91, 84, 77, 70?

• 14

• -7

• -14

• 7

What is the common difference in the sequence 7, 11, 15, 19?

• 4

• 2

• 6

• 8

What is the sixth term in the sequence defined by the recursive formula a_n = a_(n-1) - 7, where a_1 = 91?

• 70

• 63

• 56

• 49