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如果一个数列的每一项减去它前面的一项所得的差都相等,这个数列就叫做等差数列。但对于某些数列而言,这样得出来的差并不相等,而是构成一个新的等差数列,就把它叫做二阶等差数列。如果一个数列的各项同它的前一项的差构成一个二阶等差数列,便叫做三阶等差数列。这个定义很自然可以推广到一般的情形:设r是一个正整数,所谓r阶等差数列就是这样的数列,它的各项同它的前一项的差构成一个r-1阶等差数列。二阶以上的等差数列称为高阶等差数列。
If each of a series minus the one before it produces the same difference, the series is called an arithmetic sequence. However, for some series, the differences thus obtained are not equal, but constitute a new series of arithmetic differences, which is called the second-order arithmetic series. If a series of items with the difference between the previous one constitutes a second-order arithmetic series, it is called the third-order arithmetic series. This definition is naturally generalized to the general case: let r be a positive integer, the so-called r-order arithmetic sequence is such a sequence that its terms differ from its preceding one by an r-1 order difference sequence . Second order above the arithmetic sequence called high-order arithmetic sequence.