Arithmetic Progression Calculator
The Arithmetic Progression calculator helps you find terms, sums, and other key values in a sequence where each term increases or decreases by a constant difference. It’s useful for students, teachers, and anyone dealing with number patterns in math, finance, or everyday problem solving.
Arithmetic Progression Calculator
Arithmetic Sequence and Sum Formulas
\[ \text{n-th term: } a_n = a_1 + (n – 1)d \] \[ \text{Sum of first n terms: } S_n = \frac{n}{2} \left[2a_1 + (n – 1)d\right] \]
Explanation:
- $$a_1$$ is the first term
- $$d$$ is the common difference
- $$n$$ is the number of terms
- $$a_n$$ is the n-th term
- $$S_n$$ is the sum of the first n terms
An arithmetic progression (AP) is a sequence of numbers where the difference between consecutive terms is constant. It is widely used in mathematics for solving problems related to number patterns, savings plans, installment payments, and more. For example, the sequence 2, 5, 8, 11,… has a common difference of 3. This calculator allows you to calculate the n-th term, the total sum of terms, and verify patterns in an AP using simple formulas.