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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 ... - Σελίδα 246
των Charles Davies - 1835 - 353 σελίδες
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An Introduction to Algebra: With Notes and Observations: Designed for the ...

John Bonnycastle - 1811 - 230 σελίδες
...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....

A Treatise on Algebra, in Practice and Theory: With Notes and ..., Τόμος 1

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...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...

An Introduction to Algebra: With Notes and Observations : Designed for the ...

John Bonnycastle - 1818 - 326 σελίδες
...(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...

The Complete Practical Arithmetician: Containing Several New and Useful ...

Thomas Keith - 1822 - 354 σελίδες
...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,...

An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan, Robert Adrain - 1824 - 542 σελίδες
...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...

An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan - 1824 - 550 σελίδες
...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...

The Arithmetical Expositor, Or, A Treatise on the Theory and ..., Τόμος 1

Enoch Lewis - 1824 - 92 σελίδες
...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...

An Introduction to Algebra: With Notes and Observations, Designed for the ...

John Bonnycastle - 1825 - 336 σελίδες
...-: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...

An Introduction to Algebra Upon the Inductive Method of Instruction

Warren Colburn - 1825 - 400 σελίδες
...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...

An Introduction to Algebra Upon the Inductive Method of Instruction

Warren Colburn - 1828 - 330 σελίδες
...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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