Learn how to determine the nth term of a geometric sequence

The video tutorial explains how to find the n-th rule for a geometric sequence. It begins by introducing the concept and the need for a rule to determine any term in the sequence. The instructor then labels the terms and identifies the first term. The process of calculating the ratio by dividing a term by its previous term is explained. Finally, the general rule for the sequence is derived, showing how to express any term using the first term and the ratio.

What is the purpose of finding a rule for a geometric sequence?

• To calculate the average of the sequence

• To identify the last term of the sequence

• To find any term in the sequence

• To determine the sum of the sequence

What information is needed to find the rule for a geometric sequence?

• The last term and the sum of the sequence

• The first term and the common difference

• The first term and the ratio

• The number of terms and the average

How do you find the ratio in a geometric sequence?

• By multiplying the first term by the second term

• By subtracting the first term from the second term

• By adding the first and second terms

• By dividing any term by its previous term

What is the general rule for a geometric sequence if the first term is 5 and the ratio is -1/5?

• a_n = 5 * (-1/5)^(n-2)

• a_n = 5 * (-1/5)^(n-1)

• a_n = 5 * (-1/5)^n

• a_n = 5 * (-1/5)^(n+1)

What does 'n' represent in the general rule of a geometric sequence?

• The first term of the sequence

• The ratio of the sequence

• The sum of the sequence

• Any term in the sequence