Arithmetic Series

Understanding Arithmetic Series

An arithmetic series is a sequence of numbers in which the difference of any two successive members is a constant. This constant is called the common difference.

Consider the sequence: 2, 5, 8, 11, 14... where each number is 3 more than the previous one. Here, 3 is the common difference.

Formula for the nth Term

The nth term of an arithmetic series can be found with the formula:

a_n = a₁ + (n-1)d

where:

• a_n is the nth term,
• a₁ is the first term,
• d is the common difference,
• n is the term number.

Sum of an Arithmetic Series

The sum of the first n terms of an arithmetic series (denoted as S_n) can be calculated using the formula:

S_n = n/2 × (a₁ + a_n)

Or alternatively:

S_n = n/2 [2a₁ + (n-1)d]