Math Problem Statement

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

Solution

The explicit formula for the geometric sequence is given as:

an=52n1a_n = 5 \cdot 2^{n-1}

We are tasked with finding the fourth term of the sequence, which means we need to compute a4a_4.

Substitute n=4n = 4 into the formula:

a4=5241=523=58=40a_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 nn 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 nn in the explicit formula to find the desired term in any sequence.

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Math Problem Analysis

Mathematical Concepts

Geometric Sequence
Exponential Functions
Sequences and Series

Formulas

an = 5 * 2^(n-1)

Theorems

Geometric Sequence Formula

Suitable Grade Level

Grades 9-12