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" Terms ; any three of which being given, the other two may be found. This gives rise to twenty distinct cases, a few of the more important of which will be here presented. "
A Written Arithmetic, for Common and Higher Schools: To which is Adapted a ... - Page 306
by George Augustus Walton - 1864 - 348 pages
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A Written Arithmetic, for Common and Higher Schools; to which is Adapted a ...

George Augustus Walton, Mrs. Electra Nobles Lincoln Walton - Arithmetic - 1865 - 358 pages
...&c. If the numbers decrease from the first term, the series is a Decreasing Series; e. д., 13, 11, 9, 7, 5, &c. * 4:87. In every series, five things...works on Algebra. NOTE П. — Increasing series only will be considered in this book, as rules that apply to increasing series apply to decreasing series...
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Introduction to the National Arithmetic on the Inductive System: Combining ...

Benjamin Greenleaf - Arithmetic - 1871 - 350 pages
...a series? The means? When is a series ascending? When descending ? What five things are mentioned, any three of which being given, the other two may be found ? If the last term had been given and the first required, the process would evidently have been by...
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New University Algebra: A Theoretical and Practical Treatise, Containing ...

Horatio Nelson Robinson - Algebra - 1872 - 436 pages
...two primitive equations, l = ar*~l , S—— — 5—, contain the five quantities, a, r, l, n, S, any three of which being given, the other two may be found; for, by substitution of the given values, the result will always be two equations involving but two...
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A Written Arithmetic, for Common and Higher Schools: To which is Adapted a ...

George Augustus Walton - Arithmetic - 1873 - 352 pages
...In every series, five things are to be considered ; viz., the First Term, the Last Term, the Niimber of Terms, the Common Difference, and the Sum of the...presented. NOTE I For the remaining cases, also for full discussio»s of Geometrical Progression and Annuities, the student is referred to works on Algebra....
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Manual of Algebra

William Guy Peck - Algebra - 1875 - 348 pages
...in each case is 4. 175. In any geometrical progression, there are five quantities to be considered, any three of which being given, the other two may be found. These quantities are, the first term, denoted by . . . .a, " last term, denoted by ..../, " number...
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Written Arithmetic

George Augustus Walton - 1876 - 358 pages
...12, &c. If the numbers decrease from the first term, the series If a Decreasing Series; eg, 13, 11, 9, 7, 5, &c. 487. In every series, five things are...the student is referred to works on Algebra. NOTE n. — Increasing series only will be considered in this book, as rules that apply to increasing series...
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Introduction to the National Arithmetic, on the Inductive System: Combining ...

Benjamin Greenleaf - Arithmetic - 1876 - 344 pages
...series ? The means 1 When is a series ascending 1 When descending ? What five things are mentioned, any three of which being given, the other two may be found ? If the last term had been giver and the first required, the process would evidently have been by...
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The Normal Higher Arithmetic: Designed for Common Schools, High Schools ...

Edward Brooks - Arithmetic - 1877 - 560 pages
...what is the first term ? Ann. 1024. 864. Since there are five quantities in Geometrical Progression, any three of which being given, the other two may be found, there are twenty distinct cases. 865. The rules for the eight simple cases are expressed in the following...
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The Normal Elementary Algebra: Containing the First Priniples of the Science ...

Edward Brooks - Algebra - 1888 - 344 pages
...that decrease« from left to right ; as 32, 16, 8, i, etc. ill» 7. The Terms considered are five, any three of which being given, the other two may be found. THE FIVE TEEMS. 1. The first term, a ; 3. The number of terms, n ; 2. The last term, /; 4. The ratio,...
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Robinson's Progressive Practical Arithmetic: Containing the Theory of ...

Horatio Nelson Robinson - 1888 - 372 pages
...the difference between any two adjacent terms. 450. There are five parts in an arithmetical series, any three of which being given, the other two may be found. They are as follows : the first term, last term, common difference, number of terms, and sum of all...
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