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

To find the sum of the first 10 terms of a geometric sequence, we can use the formula for the sum of the first \( n \) terms:

\[
S_n = a \frac{1 - r^n}{1 - r}
\]

Where:
- \( S_n \) is the sum of the first \( n \) terms.
- \( a \) is the first term of the sequence.
- \( r \) is the common ratio.
- \( n \) is the number of terms.

For the given sequence 4, 2, 1,...:
- \( a = 4 \)
- \( r = \frac{2}{4} = \frac{1}{2} \)
- \( n = 10 \)

Now, substitute the values into the formula:

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

Simplify the expression:

\[
S_{10} = 4

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 summation. Suitable for advanced 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