Arithmetic Sequence Calculator
Calculate the nth term and the sum of the first n terms of an arithmetic sequence. Enter the first term, common difference, and term number to get started.
Decimal places for calculations.
Results:
Sequence (first terms):
The th term (a):
Sum of the first terms (S):
Understanding Arithmetic Sequences
An arithmetic sequence is a sequence of numbers such that the difference between consecutive terms is constant. This constant difference is called the common difference, denoted as 'd'. The first term is usually denoted as 'a1'.
Formula for the nth term (an): $$ a_n = a_1 + (n-1)d $$
This formula helps you find any term in the sequence if you know the first term, the common difference, and the term number.
Formula for the sum of the first n terms (Sn): $$ S_n = \frac{n}{2} [2a_1 + (n-1)d] $$
Alternatively, using the nth term (an), the sum can also be expressed as: $$ S_n = \frac{n}{2} (a_1 + a_n) $$
Arithmetic sequences are widely used in mathematics and have applications in physics, engineering, computer science, financial analysis, and more. For example, in simple interest calculations, the interest earned each period forms an arithmetic sequence.