Arithmetic series

From AoPSWiki

An arithmetic series is a sum of consecutive terms in an arithmetic sequence. For instance,

is an arithmetic series whose value is 50.

To find the sum of an arithmetic sequence, we can write it out as so (S is the sum, a is the first term, n is the number of terms, and d is the common difference):

Now, adding vertically and shifted over one, we get

This equals , so the sum is .

Problems

Introductory Problems

• 2006 AMC 10A, Problem 9
• 2006 AMC 12A, Problem 12

Intermediate Problems

• 2003 AIME I, Problem 2

Olympiad Problem

See also

• Series
• Summation

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