Recursive Formulas and Sequences

The video tutorial introduces recursive formulas, explaining how to calculate terms using these formulas. It provides two examples: the first involves a simple recursive formula, while the second example demonstrates a more complex formula. The tutorial guides viewers through the step-by-step process of calculating terms, emphasizing the importance of understanding the relationship between terms in a sequence.

What is the general form of a recursive formula?

• a(n+1) = a(n) * b

• a(n) = a(n) + c

• a(n+1) = f(a(n))

• a(n) = a(n-1) + d

In the first example, if the first term is 1, what is the second term?

• 3

• 6

• 4

• 5

How do you calculate the third term in the first example?

• 3 times the first term plus 2

• 3 times the fourth term plus 2

• 3 times the third term plus 2

• 3 times the second term plus 2

What is the value of the fourth term in the first example?

• 51

• 54

• 52

• 53

In the second example, what is the formula for a(n)?

• a(n) = 2 * a(n-1) - 5

• a(n) = 2 * (a(n-1))^2 - 5

• a(n) = 2 * a(n-1) + 5

• a(n) = 2 * (a(n-1))^2 + 5

If the first term in the second example is 2, what is the second term?

• 3

• 6

• 4

• 5

How do you calculate the third term in the second example?

• 2 times the square of the first term minus 5

• 2 times the square of the fourth term minus 5

• 2 times the square of the second term minus 5

• 2 times the square of the third term minus 5

What is the value of the third term in the second example?

• 13

• 15

• 12

• 14

What is the value of the fourth term in the second example?

• 331

• 332

• 333

• 334

What is the purpose of using recursive formulas?

• To find the sum of a series

• To define each term based on the previous term

• To calculate the average of terms

• To find the product of a series