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" In any series of numbers in arithmetical progression, the sum of the two extremes is equal to the sum of any two terms equally distant from them; as in the latter of the above series 6 + 1=4+3, and =5+2. "
Elements of algebra, by A. Ingram and J. Trotter - Page 70
by Alexander Ingram - 1844
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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; ) confequently...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1814 - 304 pages
...The sums will be Here we discover the important property, that, 428. In an arithmetical progression, the sum of 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...
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The Teachers' Assistant, Or, A System of Practical Arithmetic: Wherein the ...

Arithmetic - 1817 - 214 pages
...called the extremes. JVote. — In any series of numbers in arithmetical progression, the sum of the two extremes is equal to the sum of any two terms equally distant from them ; as in the latter of the above series 6-fl=4-f-3, and=5-{-2. Whei. the number of terms is odd, the...
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Scientific Amusements in Philosophy and Mathematics: Including Arithmetic ...

William Enfield (M.A.) - Amusements - 1821 - 302 pages
...difference taken as many times as there are terms, before it. (22.) 2nd. The sum of the extremes is always equal to the sum of any two terms equally distant from them ; or double the mean term, if the progression contains an odd number of terms. (21.) 3rd. If the sum...
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The Teachers' Assistant: Or a System of Practical Arithmetic

Stephen Pike - Arithmetic - 1824 - 212 pages
...called the extremes. Note. — In any series of numbers in arithmetical progression, the sum of the two extremes is equal to the sum of any two terms equally distant from them; as in the latter of the above series 6 + 1=4+3, and =5+2. When the number of terms is odd, the double...
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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 term twice, and the constant difference...
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Connolly's Arithmetic: Or, The Ohio Accomptant: Being a Plain Practical ...

James L. Connolly (mathematician.) - Arithmetic - 1829 - 266 pages
...last terms are called the extremes. In a series of even numbers, the sum of the two extremes will be equal to the sum of any two terms, equally distant from them; as 2, 4, 6, 8, 10, the two extremes beinj* 2+10=12,804+8=12; but if the number of terms be odd, the...
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A Concise System of Mathematics ...

Alexander Ingram - Mathematics - 1830 - 458 pages
...y — d, y ; where the sum of any two corresponding terms is a-\-y. Cor. — The double of any term is equal to the sum of any two terms equally distant from it. PROP. III. — The sum of any number of terms in arithmetical progression is equal to the sum of...
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The Juvenile Arithmetick, and Scholar's Guide: Illustrated with Familiar ...

Martin Ruter - Arithmetic - 1831 - 190 pages
...&,c. — the common dil ference is 3. In any series in Arithmetical Progression, the sum o the two extremes is equal to the sum of any two terms equally distant from them, or equal to double the mid die term when there is an uneven number oŁ terms i lie series. Thus, in...
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The Teachers' Assistant: Or, A System of Practical Arithmetic ...

Arithmetic - 1831 - 210 pages
...called the extremes. Note. — In any series of numbers in Arithmetical progression, the sum of the two extremes is equal to the sum of any two terms equally distant from them; as in i! the latter of the above series 6+1=4+3, and =5+2. i When the number of terms is odd, the double...
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