Write the rule of a geometric sequence given 2nd and 5th term

The video tutorial explains how to find the nth rule of a geometric sequence when given two non-consecutive terms, a2 and a5. The instructor demonstrates the process of determining the common ratio and the first term, and then formulating the general rule for the sequence. The tutorial emphasizes the importance of understanding the relationship between terms and using the general formula to solve for unknowns.

What is the main challenge in finding the nth term of the geometric sequence in this problem?

• Knowing the value of n

• Finding the first term and the common ratio

• Calculating the 18th term directly

• Identifying the sequence type

Why can't we directly divide the given terms to find the common ratio?

• The terms are not in the sequence

• The terms are not consecutive

• The terms are too far apart

• The terms are both negative

How is the common ratio, r, determined in this problem?

• By using a calculator

• By guessing and checking

• By using the general formula and solving for r

• By adding the terms

What is the value of the first term, a1, once the common ratio is found?

• -1/3

• -3

• 3

• 1/3

What is the general formula for the nth term of the sequence?

• a_n = 1/3 * 3^(n-1)

• a_n = -3 * 3^(n-1)

• a_n = -1/3 * 3^(n-1)

• a_n = 3^(n-1)