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" Let us put a, the first term of a progression. d, the common difference. n, the number of terms. I, the last term. 2, the sum of all the terms. The series is then a, a + d, a + %d, ....?. Any three of the above five quantities being given, the other two... "
A School Algebra - Page 244
by Simon Newcomb - 1882 - 279 pages
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The elements of algebra

James Wood - Algebra - 1841 - 492 pages
...multiplying the sum of the first and last terms by half the number of terms. Let a be the first term, b the common difference, n the number of terms, I the last term, and s the sum of the series : Then, a + (a + b) + (a + 26) + + / = s also I + (I - b) + (I - 26) +...
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Exercises and problems in algebra [by J. Pryde] with answers

James Pryde - 1855 - 136 pages
...EQUIDIFFERENT PROGRESSION, OR ARITHMETICAL PROGRESSION. NB — Let a = the first term of an EquidifFerent Progression, d = the common difference, n = the number of terms, I = the last term, and s = the sum of the series ; theii I = a + (n - 1)«?, and A = {2a + (n - l)^}ñ i an<l from these...
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Examples in Algebra for Senior Classes: Comprising Numerous Graduated ...

James Wharton - 1860 - 176 pages
...ARITHMETIC, GEOMETRIC, AND HARMONIC PROGRESSION. IN an Arithmetic Progression, if o be the first term, d the common difference, n the number of terms, I the last term, and S the sum of n terms; then I = a + (n - 1)d, S = О + (n - l)d] — . 2 Find the sum of the following...
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Algebra

Isaac Todhunter - 1860 - 622 pages
...Progression, the first term and the common difference being supposed known. Let a denote the first term, b the common difference, n the number of terms, I the last term, s the sum of the terms. Then, 8 = a + (a + b) + (a + 26)+ ...... + I. And, by writing the series in...
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Algebra for Beginners: With Numerous Examples

Isaac Todhunter - Algebra - 1863 - 302 pages
...Progression, the first term and the common difference being supposed known. Let a denote the first term, 6 the common difference, n the number of terms, I the last term, s the sum of the terms. Then «=a + (a + 6) + (a + 26) + ...... + 1. And, by writing the series in...
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New Elementary Algebra: In which the First Principles of Analysis are ...

Benjamin Greenleaf - Algebra - 1864 - 336 pages
...common difference, and number of terms, to find the sum of the terms. Let o denote the first term, d .the common difference, n the number of terms, I the last term, and S the sum of the terms. Then, or, writing the terms in the reverse order, Therefore, by adding...
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Algebra for the Use of Colleges and Schools: With Numerous Examples

Isaac Todhunter - Algebra - 1866 - 580 pages
...Progression, the first term and tlie common difference being supposed known. Let a denote the first term, Ъ the common difference, n the number of terms, I the last term, s the sum of the terms. Then s = a+(a + b) + (a + 2b) + ...... +1. And, by writing the series in the...
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New Elementary Algebra: Designed for the Use of High Schools and Academies

Benjamin Greenleaf - Algebra - 1879 - 350 pages
...common difference, and number of terms, to find the sum of the terms. Let a denote the first term, d the common difference, n the number of terms, I the last term, and S the sum of the terms. Then. S = a + (a + d) + (a + 2 d) + ...... + I, or, \rriting the terms...
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Algebra for Schools and Colleges

Simon Newcomb - Algebra - 1884 - 576 pages
...progression of which the first term is a — 4и and the common difference 2n. Problems in Progression. 2O9. Let us put a, the first term of a progression. d,...the sum of all the terms. The series is then a, a + d, a + %d, ....?. Any three of the above five quantities being given, the other two may be found....
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Algebra for Schools and Colleges

Simon Newcomb - Algebra - 1884 - 572 pages
...progression of which the first term is a — in and the common difference 2n. Problems in Progression. 209. Let us put a, the first term of a progression. d, the common difference. n, the number of terms. I, bhe last term. 2, the sum of all the terms. The series is then a, a + d, a + Zd, . . . . I. Any three...
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