Geometric Sequences and Recursive Formulas

The video tutorial explains geometric sequences, starting with an explicit rule: G(n) = 4 * 2^(n-1). It demonstrates how to calculate sequence values using this rule, starting with 4 and multiplying by 2 to get subsequent values. The tutorial then introduces a recursive rule: G(n) = 2 * G(n-1), emphasizing that each value is derived by multiplying the previous value by 2. The starting value of 4 is highlighted as crucial for the sequence's initiation.

What is the starting value in the explicit formula for the geometric sequence discussed?

• 4

• 16

• 2

• 8

In the given sequence, what operation is repeatedly performed to progress from one term to the next?

• Add 2

• Multiply by 2

• Subtract 2

• Divide by 2

If the first term of the sequence is 4, what is the third term?

• 20

• 8

• 12

• 16

How is the recursive rule for the sequence expressed?

• G(n) = G(n-1) + 2

• G(n) = G(n-1) / 2

• G(n) = 2 * G(n-1)

• G(n) = G(n-1) - 2

What is the key operation in the recursive formula for the sequence?

• Multiplying by 2

• Subtracting 4

• Adding 4

• Dividing by 2