Geometric Sequence

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio (r).

The general form of a geometric sequence is:

a_n = a₁ * r^(n-1)

Where:

• a_n = the nth term of the sequence
• a₁ = the first term of the sequence
• r = the common ratio
• n = the term number

Common Ratio (r)

The common ratio (r) is the number by which each term is multiplied to get the next term in the sequence. It is a constant value for a geometric sequence.

nth Term of a Geometric Sequence

The nth term of a geometric sequence can be found using the formula:

a_n = a₁ * r^(n-1)

Sum of a Geometric Sequence

The sum of the first n terms of a geometric sequence can be found using the formula:

S_n = a₁ * (1 - rⁿ) / (1 - r)

Study Guide

To study geometric sequences, make sure to understand the following key concepts:

1. Identifying a geometric sequence by looking for a common ratio between terms.
2. Finding the nth term of a geometric sequence using the formula a_n = a₁ * r^(n-1).
3. Finding the sum of the first n terms of a geometric sequence using the formula S_n = a₁ * (1 - rⁿ) / (1 - r).
4. Recognizing and solving problems involving geometric sequences in real-world scenarios.

Practice solving problems involving geometric sequences to solidify your understanding of the concepts.

Good luck with your studies!