Geometric Sequences and Their Properties

The video tutorial explains how to determine the common ratio in geometric sequences and calculate the first four terms of each sequence. It covers the formula for geometric sequences, demonstrates calculations using a calculator, and provides examples with different bases and exponents. The tutorial aims to help viewers understand the process of finding terms in geometric sequences and the significance of the common ratio.

What is the formula for a geometric sequence?

• a sub n equals a sub 1 times r raised to the power of n minus one

• a sub n equals a sub 1 plus r times n

• a sub n equals a sub 1 minus r times n

• a sub n equals a sub 1 divided by r raised to the power of n

What is the common ratio in the sequence where a sub n equals 40 times 1.02 raised to the power of n minus one?

• 0.98

• 1.00

• 1.02

• 40

What is the value of a sub 2 in the sequence with a common ratio of 1.02?

• 40

• 40.8

• 41.616

• 42.44832

In the sequence a sub n equals four raised to the power of n minus two divided by three, what is the common ratio?

• 1

• 4

• 3

• 2

How do you calculate a sub 1 for the sequence with base 4?

• Multiply the base by 3

• Substitute 1 for n in the formula

• Substitute 0 for n in the formula

• Divide the base by 3

What is the value of a sub 1 in the sequence with base 4?

• 1/2

• 1/12

• 1/4

• 1/3

What is the value of a sub 2 in the sequence with base 4?

• 1/2

• 1/12

• 1/4

• 1/3

What is the value of a sub 3 in the sequence with base 4?

• 16/3

• 1/12

• 4/3

• 1/3

What is the value of a sub 4 in the sequence with base 4?

• 1/12

• 16/3

• 1/3

• 4/3

What is the exponent used to calculate a sub 4 in the sequence with base 4?

• 1

• 2

• 3

• 4