GP stands for Geometric Progression in mathematics. A geometric progression (GP) is a sequence of numbers where each term is found by multiplying the previous term by a constant factor called the common ratio.
Here's a breakdown of key characteristics:
- Common Ratio (r): The constant value that is multiplied to each term to get the next term.
- First Term (a): The initial value of the sequence.
- General Formula: The nth term of a GP is given by a r^(n-1), where a is the first term, r is the common ratio, and n is the term number.
Examples:
- Sequence: 2, 4, 8, 16, 32...
- Common Ratio (r): 2 (each term is twice the previous one)
- First Term (a): 2
- Sequence: 100, 50, 25, 12.5...
- Common Ratio (r): 0.5 (each term is half the previous one)
- First Term (a): 100
Geometric progressions have various applications in different areas of mathematics and beyond, including:
- Finance: Calculating compound interest
- Physics: Modeling exponential growth or decay
- Computer Science: Analyzing algorithms
