Geometric Sequences and Their Properties

The video tutorial explains how to identify and verify a geometric sequence by calculating the common ratio. It demonstrates the process of dividing each term by the previous one to ensure the ratio remains constant. The tutorial also covers writing the equation for the sequence using the first term and the common ratio raised to the power of n minus 1.

What is the first step in identifying a geometric sequence?

• Multiplying all terms together

• Finding the rate by dividing each term by the previous one

• Calculating the difference between terms

• Finding the sum of all terms

How do you calculate the rate in a geometric sequence?

• By multiplying the first term by the last term

• By subtracting the first term from the last term

• By dividing each term by the previous term

• By adding the first and last terms

If the second term is 15 and the first term is 5, what is the rate?

• 2

• 5

• 4

• 3

What confirms that a sequence is geometric?

• Each term divided by the previous one equals the same number

• The sum of terms is a prime number

• The sequence has more than three terms

• All terms are even numbers

What is the formula to find any term in a geometric sequence?

• First term plus rate times n

• First term times rate to the power of n minus 1

• First term times rate to the power of n

• First term divided by rate to the power of n

Why is the exponent in the formula n-1?

• To ensure the sequence is finite

• To make the calculation easier

• To account for the first term already being present

• Because the sequence starts at zero

What is the first term in the given sequence?

• 45

• 5

• 3

• 15

If the first term is 5 and the rate is 3, what is the third term?

• 15

• 45

• 135

• 405

What is the common ratio in the sequence provided?

• 3

• 2

• 5

• 4

How can you verify that a sequence is geometric?

• By confirming each term divided by the previous one equals the same number

• By checking if the sequence has an even number of terms

• By ensuring each term is a multiple of the previous one

• By checking if the sum of terms is constant