What is an explicit formula in the context of a geometric sequence? 

 a. A formula that allows you to find the nth term without knowing the previous term

 b. A formula that allows you to find the nth term only by knowing the previous term

 c. A formula that allows you to find the sum of the first n terms

 d. A formula that allows you to find the difference between consecutive terms

The correct answer is:

**a. A formula that allows you to find the nth term without knowing the previous term**

In the context of a geometric sequence, an explicit formula is one that directly expresses the \(n\)th term as a function of \(n\) without requiring the calculation of any preceding terms. For a geometric sequence, the explicit formula is given by:

\[
a_n = a_1 \times r^{(n-1)}
\]

where:
- \(a_n\) is the \(n\)th term,
- \(a_1\) is the first term,
- \(r\) is the common ratio, and
- \(n\) is the term number.

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you derive the explicit formula for a geometric sequence?
2. What is the difference between explicit and recursive formulas?
3. Can an explicit formula be used for sequences other than geometric sequences?
4. How do you find the first term of a geometric sequence if the explicit formula and \(n\) are given?
5. What happens to the terms of a geometric sequence when the common ratio \(r\) is greater than 1?

**Tip:** An explicit formula is very useful because it allows you to calculate any term in the sequence directly without calculating the preceding terms.

Explore the explicit formula in geometric sequences, allowing you to find the nth term without prior terms. Learn how to apply the formula with examples and detailed explanations. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation