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" Here we discover the important property, that, in an arithmetical progression, the sum of the extremes is equal to the sum of any other two terms equally distant from the extremes. "
An Elementary Treatise on Algebra: Designed as First Lessons in that Science - Page 204
by Horatio Nelson Robinson - 1850 - 240 pages
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A New Treatise of Arithmetick and Book-keeping ...: The Whole Illustrated ...

Alexander Malcolm - Arithmetic - 1718 - 396 pages
...Remainder is the other middle Term. Profofition 3d, IN an Arithmetical Progrejjion, (V. Definition 5th) the Sum of the Extremes is equal to the Sum of any two Terms, at equal Diilance from them ; or to double the middle Term (if the Number of Terms are odd;...
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Mathematics: Compiled from the Best Authors, and Intended to be ..., Volume 1

Samuel Webber - Mathematics - 1808 - 466 pages
...being as their circumferences, the circumferences are also in arithmetical progression. But in such a, progression the sum of the extremes is equal to the sum of each two terms, equally distant from them ; therefore the sum of the circumferences on AC and CB is...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1814 - 304 pages
...a+4<7, a + 3d, a+2d, a+d, a. The sums will be Here we discover the important property, that, 428. In an arithmetical progression, the sum of the extremes...other two terms equally distant from the extremes. In the series of numbers above, the sum of the first and the last term, of the first but one and the...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1820 - 352 pages
...will be Here we discover the important property, that, 428. In an arithmetical progression, THE SUM or THE EXTREMES IS EQUAL TO THE SUM OF ANY OTHER TWO TERMS EQUALLY DISTANT FROM THE EXTREMES. In the series of numbers above, the sum of the first and the last term, of the first but one and the...
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Elements of Arithmetic, Theoretical and Practical: Adapted to the Use of ...

Ferdinand Rudolph Hassler - Arithmetic - 1826 - 224 pages
...proportion that the sum of the extremes is equal to the sum of the means, so it is evident that here the sum of the extremes is equal to the sum of any two terms equally distant from them, for the sum of every such pair of terms must contain the first...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1827 - 352 pages
...a+4<Z,2a+4d,2a+4d,2a44rf Here we discover the important property, that, 428. In an arithmetical progression, THE SUM or THE EXTREMES IS EQUAL TO THE SUM OF ANY OTHER TWO TERMS EQUALLY DISTANT FROM THE EXTREMES. In the series of numbers above, the sum of the first and the last term, of the first but one and the...
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A Concise System of Mathematics ...

Alexander Ingram - Mathematics - 1830 - 458 pages
...the nth term is n — 1. Cor. — Hence y = a + (n — l)d, and a =y — (n — l)d. PROP. II. — The sum of the extremes is equal to the sum of any two terms equally distant from them. For any term exceeds the least, as much as its corresponding term...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1831 - 354 pages
...will be 2a+4d,2a+4d,2a+4d,2a+4d,2a+4d Here we discover the important property, that, „ 428. In an arithmetical progression, THE SUM OF THE EXTREMES IS EQUAL TO THE SUM OF ANT OTHER TWO TERMS EQUALLY DISTANT FROM THE EXTREMES. In the series of numbers above, the sum of the...
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A system of practical arithmetic, comprehending numerous rules and examples ...

Samuel YOUNG (of Manchester.) - 1833 - 272 pages
...of terms, and the sum of the series ; having any three given, the other two may be found. Theorem. The sum of the extremes is equal to the sum of any two means equally distant from them. PROBLEM I. Given the extremes and number of terms to find the...
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Examples in Arithmetic and Algebra: Collected and Arranged from TheCambridge ...

Algebra - 1834 - 182 pages
...quantities form an ascending geometric series, the sum of the first and last terms is always greater than the sum of any other two terms equally distant from the extremes. 68. Prove that if any quantities, whose differences are inconsiderable with respect to the quantities...
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