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The points ..... are used to show that some terms are left out of the expression, as it is impossible to express the whole until a particular value is given to n.
An Introduction to Algebra: Upon the Inductive Method of Instruction - Σελίδα 229
των Warren Colburn - 1844 - 276 σελίδες
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## An Introduction to Algebra: With Notes and Observations: Designed for the ...

John Bonnycastle - 1811 - 220 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 Illustrations ...

John Bonnycastle - 1813 - 428 σελίδες
...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 - 260 σελίδες
...Or, the sum of any increasing arithmetical series may be found, without considering the last term, by adding the product of the common difference by the number of terms less one to twice the first term, and then multiplying the result by half the number of terms. And, if the series...

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

John Bonnycastle - 1818 - 260 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 - 332 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 - 516 σελίδες
...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
...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 Elementary Treatise on Algebra, Theoretical and Practical ...

James Ryan, Robert Adrain - 1824 - 516 σελίδες
...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 Introduction to Algebra Upon the Inductive Method of Instruction

Warren Colburn - 1825 - 372 σελίδες
...express the whole until a 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...What is the 10th term of the series 3, 5, 7, 9, &c. 1 In this a = 3, r = 2, and n — 1=9. Z = 3 + 9 X 2 = 21. In a decreasing series, r is negative. Example....

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

John Bonnycastle - 1825 - 312 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...