Find the sum. 8+12+16+…+72

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Key Concepts

Common Difference

The common difference is the constant value added to each term of an arithmetic sequence to obtain the next term. It is crucial in determining the behavior of the sequence and is used to calculate both individual terms and the overall sum of the series.

Sum of an Arithmetic Series

The sum of an arithmetic series is calculated using a formula that often involves the number of terms, the first term, and the last term. This formula, typically expressed as n/2 times the sum of the first and last terms, provides an efficient method for summing all the terms without having to add each one individually.

Arithmetic Sequence

An arithmetic sequence is a list of numbers where each term is obtained by adding a constant difference to the previous term. This type of sequence is defined by its first term and the common difference, making it fundamental in understanding patterns and series in mathematics.

Determining the Number of Terms

Finding the number of terms in an arithmetic series involves using the formula for the nth term of the sequence, which connects the first term, the common difference, and the nth term. This step is essential for calculating the sum when the total number of terms is not explicitly provided.

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