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" ... progression, is equal to the sum of the first and last terms multiplied by half the number of terms; therefore, the sum of the moments about R, is 5,000 X 5!L.! "
A Course of Mathematics: Designed for the Use of the Officers and Cadets, of ... - Page 87
by Isaac Dalby - 1807
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The elements of algebra

Andrew Bell (writer on mathematics.) - 1839 - 500 pages
...(и — 1) 6f, which is 8 equal to a + z (424.) 1 The sum of the ternis of an equidifferent series is equal to the sum of the first and last terms multiplied by half the number of terms.1 For arranging the series in order, and also in a reverse order, as in the preceding theorem,...
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Algebra made easy

Thomas Tate (mathematical master.) - 1847 - 138 pages
...in the given series. .'. 2s =7x14; .'. s=7J^!! = 49. m This result shows that the sum of the series is equal to the sum of the first and last terms multiplied by half the number of terms. In general let it be required to find the sum of the series, s= a + (a + d) + (a + 2d)+ ... to n terms....
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Equational Arithmetic: Applied to Questions of Interest, Annuities, Life ...

W. Hipsley - Business mathematics - 1852 - 116 pages
...multiplied by one less than the number of terms." " The sum of the terms of an equidifferent series is equal to the sum of the first and last terms, multiplied by half the number of terms." First term 20 Last term 20 + 4 44 2^ half the number of terms. 88 22 110 sum of five terms. As...
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Equational arithmetic applied to questions of interest, annuities ..., Volume 1

W. Hipsley - 1852 - 122 pages
...multiplied by one less than the number of terms." " The sum of the terms of an equidifferent se'ies is equal to the sum of the first and last terms, multiplied by half the number of terms." First term 20 Last term 20 + 4 44 : 2^ half the number of terms. 88 22 110 sum of five terms. As...
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The practice and theory of arithmetic

William Frederick Greenfield - 1853 - 228 pages
...the sum of two identical series, is twice the sum of one of them. Hence twice the sum of the series is equal to the sum of the first and last terms multiplied by the number of terms : or the sum of an Arithmetic series is the sum of the first and last terms multiplied...
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A treatise on algebra, in theory and practice

James William M'Gauley - 1854 - 284 pages
...is called the greater extreme. EQUIDIFFERENT PROGRESSION. 55. The sum of an equidifferent series h equal to the sum of the first and last terms, multiplied by half the number of terms. For, it is equal to all the terms, added together. That is, a, being the lesser extreme ; b, the common...
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A Treatise on Arithmetic ...

Noble Heath - 1855 - 468 pages
...of any two corresponding terms of the series. The sum, therefore, of all the terms of both series, is equal to the sum of the first and last terms multiplied by the number of terms in one series ; and as this product is evidently just twice the sum of the terms...
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A Treatise on Arithmetic: Through which the Entire Science Can be Most ...

Noble Heath - Arithmetic - 1856 - 472 pages
...of any two corresponding terms of the series. The sum, therefore, of all the terms of both series, is equal to the sum of the first and last terms multiplied by the number of terms in one series ; and as this product is evidently just twice the sum of the terms...
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Arithmetic and Algebra in Their Principles and Application ...

Barnard Smith - 1857 - 740 pages
...a+b 26. (na-6) + (nl)a+l(-2) + 6} + &c. to n terms. hence it appears "that the sum of a series in Arithmetical Progression is equal to the sum of the first and last terms, multiplied into half the number of terms." Ex. 5. Find the 36"1 term of the series 40, 38, 36, &c., and the sum...
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Arithmetic, theoretical and practical. [With] Key

Chambers W. and R., ltd - 1859 - 344 pages
...number of terms 24. Required the lost term, Ans. 13. TlIE SUM OF THE TERMS OF AS EQUIDIFFERENT SERIES is equal to the sum of the first and last terms multiplied by half the number of terms. Take any equidifferent series, as 3, 7, 11, 15, 19, 23, consisting of any number of terms, as 6 ; then...
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