Geometric Sequences and Their Terms

The video tutorial explains how to find the formula and first three terms of a geometric sequence given the 16th term and common ratio. It starts by introducing the problem and the geometric sequence formula. The instructor then substitutes the given values to solve for the first term and derives the sequence formula. The video continues by calculating the first three terms using the formula and concludes by highlighting the pattern of multiplying by the common ratio.

What is the 16th term of the geometric sequence given in the problem?

• 2,048

• 512

• 4,096

• 1,024

What is the common ratio of the sequence?

• 4

• 1

• 3

• 2

What is the general form of a geometric sequence formula?

• A_n = A_1 + R^(n-1)

• A_n = A_1 - R^(n-1)

• A_n = A_1 * R^(n-1)

• A_n = A_1 / R^(n-1)

How do you find the first term of the sequence using the given 16th term?

• Divide by 2^15

• Multiply by 2^15

• Add 2^15

• Subtract 2^15

What is the value of the first term (A_1) in the sequence?

• 1/128

• 1/16

• 1/32

• 1/64

What is the formula for the sequence after finding the first term?

• A_n = 1/64 * 2^(n-1)

• A_n = 1/128 * 2^(n-1)

• A_n = 1/16 * 2^(n-1)

• A_n = 1/32 * 2^(n-1)

How do you find the second term of the sequence using the formula?

• Multiply A_1 by 2

• Divide A_1 by 2

• Subtract 2 from A_1

• Add 2 to A_1

What is the value of the second term (A_2) in the sequence?

• 1/8

• 1/4

• 1/32

• 1/16

What is the value of the third term (A_3) in the sequence?

• 1/4

• 1/8

• 1/16

• 1/32

What pattern is used to find consecutive terms in the sequence?

• Add 2

• Multiply by 2

• Divide by 2

• Subtract 2