Exploring Formulas for Arithmetic and Geometric Sequences

Mr. Allen introduces sequences, focusing on arithmetic and geometric types. He explains how to find the first four terms of each sequence, derive explicit and recursive formulas, and provides examples for both arithmetic and geometric sequences. The arithmetic sequence example uses a common difference of five, while the geometric sequence example uses a common ratio of four. The video emphasizes understanding the formulas and their applications.

What is the common difference in the arithmetic sequence discussed?

• 5

• 4

• -12

• 12

What is the first term of the arithmetic sequence?

• -7

• 5

• -12

• 3

What is the fourth term of the arithmetic sequence?

• -7

• 8

• -2

• 3

How is the explicit formula for the arithmetic sequence expressed?

• a_n = 5n - 17

• a_n = -12 + 5(n - 1)

• a_n = 5n + 12

• a_n = -12n + 5

What is the recursive formula for the arithmetic sequence?

• a_n = 5a_(n-1) - 12

• a_n = a_(n-1) - 5

• a_n = a_(n-1) + 5

• a_n = 5a_(n-1)

What is the common ratio in the geometric sequence discussed?

• 2

• 4

• 8

• 1

What is the first term of the geometric sequence?

• 1

• 8

• 2

• 4

What is the fourth term of the geometric sequence?

• 32

• 16

• 128

• 8

How is the explicit formula for the geometric sequence expressed?

• a_n = 4 * 2^(n-1)

• a_n = 4^n

• a_n = 2 * 4^(n-1)

• a_n = 2^n

What is the recursive formula for the geometric sequence?

• a_n = 2 * a_(n-1)

• a_n = a_(n-1) + 4

• a_n = a_(n-1) * 2

• a_n = 4 * a_(n-1)