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.

The general form of a geometric sequence is:

a, ar, ar², ar³, ...

where:

• a = the first term
• r = the common ratio

Finding the nth term of a geometric sequence

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

a_n = a * r^(n-1)

where:

• a_n = the nth term
• a = the first term
• r = the common ratio
• n = the term number

Sum of the first n terms of a geometric sequence

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

S_n = a * (1 - rⁿ) / (1 - r)

where:

• S_n = sum of the first n terms
• a = the first term
• r = the common ratio
• n = the number of terms

Study Guide

1. Understand the concept of a geometric sequence.
2. Be able to identify the first term and the common ratio in a given geometric sequence.
3. Practice finding the nth term of a geometric sequence using the formula a_n = a * r^(n-1).
4. Practice finding the sum of the first n terms of a geometric sequence using the formula S_n = a * (1 - rⁿ) / (1 - r).
5. Work on problems involving real-life applications of geometric sequences, such as population growth or depreciation of assets.

By understanding the concept of geometric sequences and practicing the formulas and problem-solving, you can master this topic!