find the 11th term of geometric sequence -17,-17,-17

To find the 11th term of a geometric sequence, we use the formula for the nth term of a geometric sequence:

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

Where:
- \( a_n \) is the nth term.
- \( a_1 \) is the first term.
- \( r \) is the common ratio.
- \( n \) is the term number.

In the sequence \(-17, -17, -17, \dots\), we observe that all terms are identical. This implies that the common ratio (\(r\)) is 1, as each term is multiplied by 1 to get the next term.

Thus, the formula simplifies to:

\[
a_{11} = -17 \cdot 1^{(11-1)} = -17 \cdot 1 = -17
\]

So, the 11th term is \(-17\).

Would you like further explanation or have any other questions?

Here are 5 related questions to expand your understanding:
1. How do you find the common ratio in a geometric sequence?
2. What happens if the common ratio in a geometric sequence is negative?
3. How do you find the sum of the first n terms of a geometric sequence?
4. What is the formula for the sum of an infinite geometric series?
5. How do you differentiate between an arithmetic and a geometric sequence?

**Tip**: In a geometric sequence, if all terms are identical, the common ratio is always 1.

Discover how to calculate the 11th term of the geometric sequence -17, -17, -17 using the formula for the nth term. Learn about geometric sequences, the common ratio, and how constant values affect a sequence. This explanation is ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation