Recursive Sequences and Rules

The video tutorial explains a series of calculations starting with F of 0 equal to -12. Each subsequent value is found by subtracting 7 from the previous value, forming a recursive sequence. The rule for this sequence is F of n equals F of n-1 minus 7. This recursive rule is used to find any value in the sequence by consistently applying the subtraction of 7.

What is the initial value of the series?

• -12

• 7

• 0

• 12

How do you find the value of F(1) from F(0)?

• Divide F(0) by 7

• Multiply F(0) by 7

• Subtract 7 from F(0)

• Add 7 to F(0)

What operation is repeatedly used to find the next value in the series?

• Division

• Multiplication

• Subtraction

• Addition

What is the recursive rule for finding any value in the series?

• f(n) = f(n-1) + 7

• f(n) = f(n-1) - 7

• f(n) = f(n-1) * 7

• f(n) = f(n-1) / 7

If F(2) is known, how can F(3) be calculated?

• Multiply F(2) by 7

• Subtract 7 from F(2)

• Divide F(2) by 7

• Add 7 to F(2)

What does the recursive rule help us determine?

• The initial value of the series

• The sum of all values in the series

• The next value by adding 7

• Any value in the series by using the previous value

What is the purpose of the recursive rule in this context?

• To calculate any value based on the previous one

• To multiply each value by 7

• To determine the initial value

• To find the sum of the series