Key Concepts & Glossary
Key Equations
recursive formula for nth term of an arithmetic sequence | {a}_{n}={a}_{n - 1}+d\phantom{\rule{1}{0ex}}n\ge 2 |
explicit formula for nth term of an arithmetic sequence |
Key Concepts
- An arithmetic sequence is a sequence where the difference between any two consecutive terms is a constant.
- The constant between two consecutive terms is called the common difference.
- The common difference is the number added to any one term of an arithmetic sequence that generates the subsequent term.
- The terms of an arithmetic sequence can be found by beginning with the initial term and adding the common difference repeatedly.
- A recursive formula for an arithmetic sequence with common difference is given by .
- As with any recursive formula, the initial term of the sequence must be given.
- An explicit formula for an arithmetic sequence with common difference is given by .
- An explicit formula can be used to find the number of terms in a sequence.
- In application problems, we sometimes alter the explicit formula slightly to .
Glossary
- arithmetic sequence
- a sequence in which the difference between any two consecutive terms is a constant
- common difference
- the difference between any two consecutive terms in an arithmetic sequence