An Introduction to Algebra Being the First Part of a Course of Mathematics Ad
An Introduction to Algebra Being the First Part of a Course of Mathematics Ad
Jeremiah Day
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The sum of bath the series is, therefore, twice as great, as the sum of the terms in one of them. There is an easy method of finding this double sum, and of course, the sum itself which is the object of inquiry. Let a given series be written, both in the direct, and in the in- verted order, and then add the corresponding terms together;, ARITHMETICAL PROGRESSION. 21? Take, for instance, the series 3, 5, 7, 9, 11 And the same inverted 11, 9, 7, 5, 3. The sums of the terms will be 14, 14, 14, 14,... 14. Take also the series a, a-\-d, a+2d, a-\-3d, a+4c?, And the same inver. A-{-4d, a-j-3rf, a-\-%d, a-{-d, a. The sums will be 2a+4d, 2a+4d, Za+4d, 2a+4d, 2a-{-4d Here we discover the important property, that, 428. In an arithmetical progression, THE SUM OF THE EX- TREMES IS EQUAL TO THE SUM OF ANY OTHER TWO TERMS EQUALLY DISTANT FROM THE EXTREMES. In the series of numbers above, the sum of the first and the last term, of the first but one and the last but one, &c. Is 14. And in the other series, the sum of each pair of corres- ponding terms is 2a-\-4d.
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