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" That is : The first term of an increasing arithmetical progression is equal to the last term, minus the product of the common difference by the number of terms less one. "
Elements of Algebra: Tr. from the French of M. Bourdon. Revised and Adapted ... - Page 246
by Charles Davies - 1835 - 353 pages
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An Introduction to Algebra: With Notes and Observations: Designed for the ...

John Bonnycastle - Algebra - 1811 - 230 pages
...III. The last term of any arithmetical series is equal to the sum or difference of the first term, and the product of the common difference by the number of terms less , one ; according as the series is increasing or decreasing. Thus, the 20th term of 2, 4, 6, 8, 10, 12, &c....
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A Treatise on Algebra, in Practice and Theory: With Notes and ..., Volume 1

John Bonnycastle - Algebra - 1813 - 456 pages
...2 x (a+2d). 5. The last term of any increasing arithmetical series is equal to the first term plus the product of the common difference by the number of terms less one ; and if the series be decreasing, it will he equal to the first term minus that product. Thus, the...
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An Introduction to Algebra: With Notes and Observations : Designed for the ...

John Bonnycastle - Algebra - 1818 - 326 pages
...(a+4d)=(a+d)+(a+3d)=2 X(o+2«i). 5. The last term of any increasing arithmetical series is equal to the first term plus the product of the common difference by the number of terms less one ; and if the series be decreasing, it will be equal to the first term minus that product. Thus, the...
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The Complete Practical Arithmetician: Containing Several New and Useful ...

Thomas Keith - Arithmetic - 1822 - 354 pages
...13- &c- be 'n arithmetical progression, then will 4. The difference between the extremes is equal to the product of the common difference by the number of terms less one> Thus, if 3. 5. 7. 9. &c. be in arithmetical progression, Tlien will 9—3=2x4—15. The number of terms,...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...rest of the terms. Hence the last term of any arithmetical series is equal to the first term plus or minus, the product of the common difference, by the number of terms less one. 469. Also, if s be put equal to the sum of any number of terms of this progression, we shaU have And...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan - Algebra - 1824 - 550 pages
...rest of the terms. Hence the last term of any arithmetical series is equal to the. first term plus or minus, the product of the common difference, by the number of terms less one. 469. Also, if s be put equal to the sum of any number of terms of this progression, we shall have And...
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The Arithmetical Expositor, Or, A Treatise on the Theory and ..., Volume 1

Enoch Lewis - Arithmetic - 1824 - 92 pages
...subsequent term, it is manifest that the whole sum, by which the first term is increased or diminished, is the product of the common difference by the number of terms less one. (48.) The sum of the extremes is evidently equal to the sum of the second from thebeginning, and the...
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An Introduction to Algebra: With Notes and Observations, Designed for the ...

John Bonnycastle - Algebra - 1825 - 336 pages
...-:d)= x (a+td.) 5. The last term of any increasing arithmetical series is equal to the first term plus the product of the common difference by the number of terms less one ; and it ^ the series be decreasing, it will be equal to the first term minus that product. Thus, the...
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An Introduction to Algebra Upon the Inductive Method of Instruction

Warren Colburn - Algebra - 1825 - 400 pages
...particular value is given to «. Let I be the term required, then Hence,any term may be found by adding the product of the common difference by the number of terms less one, to the first term. Example. What is the 10th term of the series 3, 5, 7, 9, &c. 1 In this a = 3, r...
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An Introduction to Algebra Upon the Inductive Method of Instruction

Warren Colburn - Algebra - 1828 - 330 pages
...to express the whole until a particular value is given to n. Hence, any term may be found by adding the product of the common difference by the number of terms less one, to the first term. Example. What is the 10th term of the series 3, 5, 7, 9, &c. In this a = 3, r =...
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