Question

What is geometric sequence and it's example

Answer 1

A geometric sequence (or geometric progression) 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.

In mathematical terms, a geometric sequence can be represented as:
- \( a, ar, ar^2, ar^3, \ldots \)
Where:
- \( a \) is the first term,
- \( r \) is the common ratio,
- \( n \) is the term number.

### Example:
Consider the geometric sequence where the first term \( a = 3 \) and the common ratio \( r = 2 \).

The terms of this sequence would be:
1. First term: \( 3 \) (which is \( a \))
2. Second term: \( 3 \times 2 = 6 \)
3. Third term: \( 6 \times 2 = 12 \)
4. Fourth term: \( 12 \times 2 = 24 \)
5. Fifth term: \( 24 \times 2 = 48 \)

So, the sequence is:
**3, 6, 12, 24, 48, ...**

Each term is obtained by multiplying the previous term by the common ratio of 2.