An arithmetic series is the sum of the terms of an arithmetic sequence, where each term after the first is obtained by adding a constant difference to the previous term. The sum can be calculated using the formula S_n = n/2 * (a_1 + a_n), where S_n is the sum of the first n terms, a_1 is the first term, and a_n is the nth term.

Arithmetic Series

arithmetic series

sum of the terms

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant, known as the common difference. This type of sequence is linear in nature and can be expressed using the formula for the nth term: an = a1 + (n-1)d, where a1 is the first term and d is the common difference.

arithmetic sequence

The concept of 'constant difference' refers to a situation where the difference between consecutive terms in a sequence remains the same, characteristic of an arithmetic sequence. This regularity is fundamental in identifying linear relationships and can be used to predict subsequent terms and analyze patterns in data sets.

constant difference

previous term

formula S_n

sum of the first n terms

The 'First Term' typically refers to the initial period of an academic year or the first segment of a political leader's tenure. It sets the foundation for future progress, establishing priorities and setting the tone for subsequent terms or periods.

first term

The 'Nth Term' refers to a formula that allows you to find any term in a sequence without listing all the terms. It is crucial for understanding patterns in sequences and enables efficient calculation of terms in arithmetic and geometric sequences.

CUSTOMIZE YOUR LEARNING

CUSTOMIZE YOUR LEARNING

Relevant Fields: