Geometric Sequences and Rules

The video tutorial explains how to write a geometric sequence recursively by reviewing the explicit rule. It covers the explicit rule for geometric sequences, the concept of common ratio, and how to find terms in a sequence using both explicit and recursive rules. The tutorial also highlights common mistakes when using recursive rules and demonstrates that both rules yield the same results through examples.

What is the recursive rule for a sequence where the common ratio is 3?

• a_n = 3 * a_(n-1)

• a_n = 3 * n

• a_n = 4 * n

• a_n = 4 * a_(n-1)

How do you find the eighth term in a geometric sequence using the explicit rule?

• Multiply the first term by the common ratio raised to the power of 8

• Add the first term to the common ratio raised to the power of 8

• Multiply the first term by the common ratio raised to the power of 7

• Add the first term to the common ratio raised to the power of 7

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

• Identify the first term and the last term

• Identify the last term and the common ratio

• Identify the first term and the common ratio

• Identify the common ratio and the sequence length

What is the result of using the explicit rule to find the eighth term in the sequence?

• 128

• 512

• 256

• 384

In a recursive sequence, how is each term found?

• By dividing the previous term by a constant

• By subtracting a constant from the previous term

• By multiplying the previous term by a constant

• By adding a constant to the previous term

What is the common ratio in a sequence where each term is multiplied by 3?

• 5

• 3

• 4

• 2

What is a common mistake when evaluating recursive rules?

• Using division instead of multiplication

• Confusing the common ratio with the first term

• Using addition instead of multiplication

• Confusing the sequence order

What is the explicit rule for a geometric sequence with a first term of 4 and a common ratio of 3?

• a_n = 3 + 4^(n-1)

• a_n = 3 * 4^(n-1)

• a_n = 4 + 3^(n-1)

• a_n = 4 * 3^(n-1)

How do you find the fifth term using the explicit rule?

• a_5 = 4 + 3^4

• a_5 = 4 * 3^4

• a_5 = 3 * 4^5

• a_5 = 3 + 4^5

What is the value of the fifth term using the recursive rule if the fourth term is 108?

• 108

• 432

• 216

• 324