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" The difference of the extremes divided by the number of the terms less 1, gives the common difference; consequently, the same divided by the common difference must give the number of terms less 1 : hence, this quotient augmented by 1, must give the number... "
A System of Arithmetic: Reprinted from the Mathematical Text-book - Page 172
by Samuel Webber - 1812 - 248 pages
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Mathematics: Compiled from the Best Authors and Intended to be the ..., Volume 1

Mathematics - 1801 - 446 pages
...EXAMPLES. * By the last problem,' the difference of the extremes, divided by the number of terms less i, gives the common difference ; consequently the same,...the number' of terms less i ; hence this quotient, augmented by I, must be the answer to the question. In any arithmetical progression, the sum of any...
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Mathematics: Compiled from the Best Authors, and Intended to be ..., Volume 1

Samuel Webber - Mathematics - 1808 - 466 pages
...of the extremes, divided by the number of terms less 1, gives the common difference ; cpnsequently the same, divided by the common difference, must give the number. of terms less 1 ; hence this quotient, augmented by 1 , must be the answer to the question. 155 EXAMPLES. 1. The...
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The Youth's Assistant in Theoretick and Practical Arithmetic

Zadock Thompson - Arithmetic - 1826 - 176 pages
...separately ; whence the rule ig manifest. t By Problem II. the difference of the extremes, divided by the' number of terms, less 1, gives the common difference ; consequently, tint same divided by the common difference, must give the number of terms less 1 -, hence this qootieot,...
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A New and Complete System of Arithmetick: Composed for the Use of the ...

Nicolas Pike - Arithmetic - 1832 - 544 pages
...* By the first Problem the difference of the extremes, divided by the number of terms less 1, gave the common difference; consequently the same divided...common difference, must give the number of terms less 1 ; hence, this quotient, augmented by 1, must be the answer to the question. t By the 3d Problem find...
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The Youth's Assistant in Theoretic and Practical Arithmetic: Designed for ...

Zadock Thompson - Arithmetic - 1832 - 186 pages
...of terms, less 1-^ gives the common difference (277) ; consequently the difference of the extremes divided by the common difference, must give the number of terms, less 1 (11— 3=8, and 8-f2rr4, and 4+1—) 5 Ans. Hence, III. The first term, the last term, and the common...
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The Youth's Assistant in Theorhetic [sic] and Practical Arithmetic: Designed ...

Zadock Thompson - Arithmetic - 1832 - 182 pages
...of terms, less 1, gives the common difference (277) •, consequently the difference of the extremes divided by the common difference, must give the number of terms. less 1 (11—3—8, and 8-f-2=t, and 4+1=) 5 Ans. Hence, III. The first term, the lost term, and the common-...
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The North American Arithmetic: Part Third, for Advanced Scholars, Volume 3

Frederick Emerson - Arithmetic - 1834 - 300 pages
...quotient; the sum will be the number of terms. The difference of the extremes divided by the number of the terms less 1, gives the common difference; consequently,...common difference must give the number of terms less 1 : hence, this quotient augmented by 1, must give the number of terms. 8. The extremes in an equidifferent...
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The North American Arithmetic: For Advanced Scholars. part third

Frederick Emerson - Arithmetic - 1839 - 300 pages
...quotient; the sum will be the number of terms. The difference of the extremes divided by the number of the terms less 1, gives the common difference; consequently,...common difference must give the number of terms less 1 : hence, this quotient augmented by 1, must give the number of terms. 8. The extremes in an equidifferent...
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A manual of arithmetic

George Hutton (arithmetic master, King's coll. sch.) - 1844 - 276 pages
...divided by the number of terms less 1 gives the common differences; so the difference of the extremes divided by the common difference must give the number of terms less 1, to which, if we add I, the sum will be the number of terms required. Hence the The two extremes...
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The scholar's guide to arithmetic; or, A complete exercise-book

John Bonnycastle - 1851 - 314 pages
...one, gives the common difference, according to the last problem, it follows that the same difference divided by the common difference, must give the number of terms less one ; whence this quotient, augmented by one, must be the number of terms, which is the same at the...
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