What is the sum of the first 10 terms of the geometric sequence 4,2,1??

The given geometric sequence is \( 4, 2, 1, \dots \), where:

- The first term \( a = 4 \),
- The common ratio \( r = \frac{2}{4} = \frac{1}{2} \).

The formula for the sum \( S_n \) of the first \( n \) terms of a geometric sequence is:

\[
S_n = \frac{a(1 - r^n)}{1 - r} \quad \text{for} \, |r| < 1.
\]

Here:
- \( a = 4 \),
- \( r = \frac{1}{2} \),
- \( n = 10 \).

Substituting these values:

\[
S_{10} = \frac{4 \left(1 - \left(\frac{1}{2}\right)^{10}\right)}{1 - \frac{1}{2}}.
\]

Simplifying:

\[
S_{10} = \frac{4 \left(1 - \frac{1}{1024}\right)}{\frac{1}{2}} = \frac{4 \left(\frac{1023}{1024}\right)}{\frac{1}{2}} = 4 \times \frac{1023}{1024} \times

Learn how to calculate the sum of the first 10 terms of the geometric sequence 4, 2, 1 using the sum of geometric series formula. This problem covers key concepts in geometric sequences and series, including the common ratio and the formula for the sum of terms. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation