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" The sum of any number of terms is equal to the sum of the extremes multiplied by half the number of terms. "
Elements of algebra, by A. Ingram and J. Trotter - Page 70
by Alexander Ingram - 1844
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A New Treatise of Arithmetick and Book-keeping ...: The Whole Illustrated ...

Alexander Malcolm - Arithmetic - 1718 - 396 pages
...this Propafition, it follows clearly, that the Sum of all the Terms of an Arithmetical Progreffion, is equal to the Sum of the Extremes multiplied by half the Number of Terms; but if that Number is odd, multiply the forefaid Sum, by that whole Number ; and half the Product is...
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Scientific Amusements in Philosophy and Mathematics: Including Arithmetic ...

William Enfield (M.A.) - Amusements - 1821 - 302 pages
...;4 + 8 = 2x6 ^ In the first case, the sum of an arithmetical progression, is equal to the product of the sum of the extremes multiplied' by half the number of terms; and in the second, to the product of the mean multiplied by the number of terms. THEOREM III. 23. In...
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A New and Complete System of Arithmetick: Composed for the Use of the ...

Nicolas Pike - Arithmetic - 1822 - 536 pages
...equal to the mean (or half the sum of the two extremes) multiplied by the whole number of terms ; or to the sum of the extremes multiplied by half the number of terms. The sum of auy number of terms of the arithmetical series of odd numbers 1 , 3, 5, 7, 9, &r.. is equal...
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A Concise System of Mathematics ...

Alexander Ingram - Mathematics - 1830 - 458 pages
...equally distant from it. PROP. III. — The sum of any number of terms in arithmetical progression is equal to the sum of the extremes multiplied by...number of terms of the series. Cor. 1. — Hence if * = sum of the series, s = (a+_y)|-. Cor. 2. — If the number of terms be .odd, and m the middle one,...
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Elements of Algebra

Bourdon (M., Louis Pierre Marie) - Algebra - 1831 - 326 pages
...finally S. = that is, the sum of the terms of a progression by difference is equal to the product of the sum of the extremes multiplied by half the number of terms. If, in this formula, we substitute for I its value a + (n — 1) r, we obtain further o_[2a+ (-l)r]n....
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An Elementary Treatise on Algebra, Theoretical and Practical: With Attempts ...

John Radford Young - Algebra - 1832 - 408 pages
...latter a — (n — l)d. THEOREM 5. The sum of any series of quantities in arithmetical progression is equal to. the sum' of the extremes multiplied by half the number of terms. Let a + (a + d) + (a + 2d) + (a + 3d) + &c., be the progression ; then if the number of terms be represented...
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A New and Complete System of Arithmetick: Composed for the Use of the ...

Nicolas Pike - Arithmetic - 1832 - 544 pages
...equal tome mean (or half the sum of tiie two extremes) multiplied by the whole numbor of terms ; or to the sum of the extremes multiplied by half the number of teruw. The sum of any nmnlfr of terms of the arithmetical series of odd number* 1, 3, 5, 7, 9, ,tc....
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A system of practical arithmetic, comprehending numerous rules and examples ...

Samuel YOUNG (of Manchester.) - 1833 - 272 pages
...the difference of the extremes divided by the number of terms minus one. And the sum of the series is equal to the sum of the extremes multiplied by half the number of terms. (1) Given the extremes 12 and 42, and the number of terms 11. Required the common difference, and sum...
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The North American Arithmetic: Part Third, for Advanced Scholars, Volume 3

Frederick Emerson - Arithmetic - 1834 - 300 pages
...multiplied by the number of terms and divided by 2; or, which amounts to the same, the sum of all the terms is equal to the sum of the extremes multiplied by half the the number of terms. For example, the sum of the following series, 2, 4, 6, 8, 10, 12, 14, 16, is 2...
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A Practical and Theoretical System of Arithmetic...: Also, a Treatise on ...

George Willson - Arithmetic - 1836 - 202 pages
...the reason of this proposition is evident. PROPOSITION III. The sum of all the terms of the series, is equal to the sum of the extremes multiplied by half the number of terms ; or, multiplied by the number of terms, and the product divided by 2. For example, 1, 3, 5, 7, 9,...
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