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Sequences and Series

Arithmetic Sequences

Problems

Problems

An arithmetic sequence is a sequence in which the difference between each consecutive term is constant. An arithmetic sequence can be defined by an explicit formula in which a n = d (n - 1) + c , where d is the common difference between consecutive terms, and c = a 1 . An arithmetic sequence can also be defined recursively by the formulas a 1 = c, a n+1 = a n + d , in which d is again the common difference between consecutive terms, and c is a constant.

The sum of an infinite arithmetic sequence is either , if d > 0 , or - ∞ , if d < 0 .

There are two ways to find the sum of a finite arithmetic sequence. To use the first method, you must know the value of the first term a 1 and the value of the last term a n . Then, the sum of the first n terms of the arithmetic sequence is S n = n() . To use the second method, you must know the value of the first term a 1 and the common difference d . Then, the sum of the first n terms of an arithmetic sequence is S n = na 1 + (dn - d ) .

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