How to determine the rule for a geometric sequence given two values

The video tutorial explains how to identify the first five terms of a geometric sequence by using the formula a_n = a_1 * r^(n-1). It begins with an introduction to geometric sequences and the importance of finding the common ratio, r. The instructor demonstrates how to solve for r using given terms and then applies the formula to calculate the first five terms of the sequence. The tutorial concludes with a review of the calculations and a final answer for the fifth term.

What is the formula for a geometric sequence?

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

• a sub n equals a sub 1 plus d times n minus 1

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

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

What is the value of the common ratio, r, in the given sequence?

• 4/5

• 2/3

• 3/4

• 1/2

What is the second term of the sequence if the first term is 9 and the common ratio is 2/3?

• 4

• 5

• 6

• 3

What is the fourth term of the sequence?

• 8/3

• 9

• 16/9

• 4

What is the fifth term of the sequence?

• 9

• 16/9

• 4

• 8/3