What is a Geometric Sequence?
- A geometric sequence/progression is like an arithmetic sequence, except the difference between terms is not constant.
- Each term is instead multiplied by a constant term, which is called the common ratio.
- The common ratio is denoted by r.
- A geometric sequence follows the pattern:
u, ur, ur², ur³, ur⁴, ...
- Where u is the initial value and r is the common ratio.
- Each time the previous term is multiplied by the common ratio, r, to make the new term.
Geometric Series
- A geometric series is like a geometric sequence but all the individual terms are summed together.
- It looks like:
u + ur + ur²+ ur³ + ur⁴, ...
- Where u is the initial value and r is the common ratio.
- The sum can be calculated as:
- Geometric series are often used to calculate compound interest whereas arithmetic series might be used to calculate simple interest.