Geometric Sequences and Formulas

The video tutorial explains how to model a geometric sequence using both recursive and explicit rules. It starts by identifying the recursive rule, which involves multiplying the previous term by a constant factor. The sequence given is 5, 10, 20, and 40, with a common ratio of 2. The recursive formula is G(n) = 2 * G(n-1). The tutorial then moves on to derive the explicit rule, which is G(n) = 5 * 2^(n-1), where 5 is the initial value and 2 is the growth factor. This formula allows calculation of any term in the sequence based on its position.

What is the first step in finding the recursive rule for a geometric sequence?

• Determine the number of terms

• Find the sum of the sequence

• Identify the common ratio

• Identify the common difference

In the sequence 5, 10, 20, 40, what operation is used to move from one term to the next?

• Divide by 2

• Add 5

• Multiply by 2

• Subtract 5

What is the recursive formula for the sequence 5, 10, 20, 40?

• G(n) = G(n-1) + 5

• G(n) = 2 * G(n-1)

• G(n) = G(n-1) - 5

• G(n) = G(n-1) / 2

What is the initial value in the explicit formula for the sequence 5, 10, 20, 40?

• 40

• 5

• 20

• 10

What is the growth factor in the explicit formula for the sequence 5, 10, 20, 40?

• 2

• 20

• 10

• 5

How is the number of times to multiply by the growth factor determined in the explicit formula?

• By the common difference

• By the sum of the sequence

• By the term number minus one

• By the initial value

What does the 'n-1' represent in the explicit formula G(n) = 5 * 2^(n-1)?

• The number of multiplications

• The term number

• The initial value

• The common ratio

Which formula allows you to find any term in the sequence directly?

• Recursive formula

• Explicit formula

• Arithmetic formula

• Summation formula

What is the explicit formula for the sequence 5, 10, 20, 40?

• G(n) = 5 / 2^(n-1)

• G(n) = 5 - 2^(n-1)

• G(n) = 5 * 2^(n-1)

• G(n) = 5 + 2^(n-1)

What is the purpose of the explicit formula in a geometric sequence?

• To find the number of terms

• To find any term directly

• To find the common difference

• To find the sum of the sequence