Geometric Sequences and Ratios

The video tutorial explains how to find the first four terms and the common ratio of geometric sequences. It provides two examples, detailing the step-by-step process of calculating terms and determining the common ratio. The first example uses a sequence defined by a formula involving powers of 2 and 3, while the second example uses powers of 6. The tutorial emphasizes understanding the pattern of multiplying by the common ratio to find subsequent terms.

What is the first step in finding the common ratio of a geometric sequence?

• Calculate the first term

• Multiply the first term by the common ratio

• Divide any term by the previous term

• Subtract the first term from the second term

What is the value of the first term (a1) in the first sequence?

• 1/3

• 2/3

• 1/2

• 3/2

How is the second term (a2) calculated in the first sequence?

• 2^1 / 3^2

• 2^2 / 3^2

• 2^1 / 3^1

• 2^2 / 3^1

What is the common ratio of the first sequence?

• 3/2

• 1/2

• 1/3

• 2/3

What is the formula used to find the common ratio in a geometric sequence?

• a_n / a_(n-1)

• a_(n-1) / a_n

• a_n * a_(n-1)

• a_n + a_(n-1)

What is the first term (a1) in the second sequence?

• 1/72

• 1/12

• 1/36

• 1/6

How is the second term (a2) calculated in the second sequence?

• 6^-1 / 2

• 6^0 / 2

• 6^1 / 2

• 6^2 / 2

What is the value of the third term (a3) in the second sequence?

• 1

• 1/2

• 1/12

• 1/6

What is the common ratio of the second sequence?

• 3

• 6

• 12

• 2

How is the common ratio verified in the second sequence?

• By subtracting a3 from a4

• By multiplying a3 by a4

• By dividing a4 by a3

• By adding a3 and a4