https://file.aiquickdraw.com/mathbot/file/1727118589532y1nlzebf.jpg

The explicit formula for the geometric sequence is given as:

\[
a_n = 5 \cdot 2^{n-1}
\]

We are tasked with finding the fourth term of the sequence, which means we need to compute \(a_4\). 

Substitute \(n = 4\) into the formula:

\[
a_4 = 5 \cdot 2^{4-1} = 5 \cdot 2^3 = 5 \cdot 8 = 40
\]

So, the fourth term of the sequence is **40**.

Would you like a detailed explanation of how geometric sequences work? Here are 5 related questions that may help expand your understanding:

1. How do you find the common ratio in a geometric sequence?
2. What is the general formula for the nth term of a geometric sequence?
3. How can you determine the sum of the first \(n\) terms of a geometric sequence?
4. What is the difference between geometric and arithmetic sequences?
5. How would you find the fifth term of this same sequence?

**Tip:** Always ensure to substitute the correct value of \(n\) in the explicit formula to find the desired term in any sequence.

The explicit formula for a geometric sequence is an = 5 * 2^(n-1). What is the fourth term of the sequence?

Discover how to find the fourth term of a geometric sequence using the formula an = 5 * 2^(n-1). Step-by-step solution provided, ideal for students in Grades 9-12 studying exponential sequences.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation