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In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15 … is an arithmetic progression with ''common difference'' of 2. If the initial term of an arithmetic progression is and the common difference of successive members is ''d'', then the ''n''th term of the sequence () is given by: : and in general : A finite portion of an arithmetic progression is called a finite arithmetic progression and sometimes just called an arithmetic progression. The sum of a finite arithmetic progression is called an arithmetic series. The behavior of the arithmetic progression depends on the common difference ''d''. If the common difference is: *Positive, the members (terms) will grow towards positive infinity. *Negative, the members (terms) will grow towards negative infinity. ==Sum== Computation of the sum 2 + 5 + 8 + 11 + 14. When the sequence is reversed and added to itself term by term, the resulting sequence has a single repeated value in it, equal to the sum of the first and last numbers (2 + 14 = 16). Thus 16 × 5 = 80 is twice the sum. The sum of the members of a finite arithmetic progression is called an arithmetic series. For example, consider the sum: : This sum can be found quickly by taking the number ''n'' of terms being added (here 5), multiplying by the sum of the first and last number in the progression (here 2 + 14 = 16), and dividing by 2: : In the case above, this gives the equation: : This formula works for any real numbers and . For example: : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Arithmetic progression」の詳細全文を読む スポンサード リンク
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