Recursive Sequences and Formulas

This video tutorial introduces recursively defined sequences, explaining how they differ from explicit formulas by using previous terms to define subsequent ones. It covers recursive notation, demonstrates examples of calculating terms in recursive sequences, and shows how to create recursive formulas from observed patterns. The video also explores sequences with negative multiplication and two-term dependencies, providing a comprehensive understanding of recursive sequences.

What is a recursively defined sequence?

• A sequence where each term is a random number.

• A sequence where each term is defined by referencing previous terms.

• A sequence where each term is the same as the first term.

• A sequence where each term is defined by a fixed formula.

In a sequence, what is the term before a3?

• a1

• a2

• a4

• a5

If a term in a sequence is a_n, what is the term after it?

• a_(n-1)

• a_(n+1)

• a_(n-2)

• a_(n+2)

Given the first term a1 = 3 and the recursive formula a_n = a_(n-1) + 4, what is the second term?

• 15

• 11

• 7

• 3

Using the same sequence, what is the fifth term?

• 23

• 15

• 11

• 19

Given the first term a1 = 2 and the recursive formula a_n = -5 * a_(n-1), what is the second term?

• 5

• -5

• 10

• -10

For the sequence with the first term a1 = 2 and the recursive formula a_n = -5 * a_(n-1), what is the fifth term?

• -250

• 250

• -1250

• 1250

If a sequence starts with a1 = 20 and follows the pattern a_n = a_(n-1) - 4, what is the third term?

• 8

• 4

• 16

• 12

For the sequence starting at 72 and following the pattern a_n = a_(n-1) / 2, what is the fourth term?

• 18

• 9

• 36

• 4.5

What is the recursive formula for a sequence starting at 20 and decreasing by 4 each term?

• a_n = a_(n-1) * 4

• a_n = a_(n-1) - 4

• a_n = a_(n-1) + 4

• a_n = a_(n-1) / 4