Short result:
Arithmetic Sequence Calculator
Result
Date publish: 17.09.2024
|
Author: Calcwizard
Understanding Arithmetic Sequences
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is known as the common difference. For instance, in the sequence 2, 5, 8, 11, the common difference is 3.
Formula for the nth Term
The nth term of an arithmetic sequence can be calculated using the formula:
an = a1 + (n – 1) * d
Where:
- an = nth term
- a1 = first term
- d = common difference
- n = term number
Examples of Arithmetic Sequences
| First Term (a1) | Common Difference (d) | Term Number (n) | nth Term (an) |
|---|---|---|---|
| 2 | 3 | 5 | 14 |
| 1 | 4 | 6 | 21 |
| 10 | -2 | 4 | 6 |
Interesting Facts
- The sum of the first n terms of an arithmetic sequence can also be calculated using the formula: Sn = n/2 * (a1 + an).
- Arithmetic sequences are commonly found in real-life situations, such as calculating the total distance traveled when moving at a constant speed.
- The famous mathematician Euclid studied arithmetic sequences over 2000 years ago, laying the groundwork for modern mathematics.
