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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 Upon the Inductive Method of Instruction

Warren Colburn - 1836 - 276 σελίδες
...impossible to express the whole until a particular value is given to n. Let I be the term required, then Hence, any term may be found by adding the product...series 3, 5, 7, 9, &c. In this a = 3, r = 2, and n — 1 = 9. In a decreasing series, r is negative. Example. What is the 13th term of the series 48,...

A. Turnbull - 1836 - 335 σελίδες
...above. We have seen, by the last paragraph, that the last term of the series is the first term with the product of the common difference, by the number of terms less one added to it Thus, /+ (» — I) d — I : consequently, if we subtract the first term from the last,...

## An Introduction to Algebra: Upon the Inductive Method of Instruction

Warren Colburn - 1838 - 276 σελίδες
...be found by adding the product of thecommon difference by the number of terms less one, to the iirst term. . . . ' Example. What is the 10th term of the...7, 9>. &c. In this a = 3, r — 2, and n — 1=9. . f / = 3 + 9 X2=21. In a decreasing series, r is negative. Example. What is the 13th term of the series...

## Elements of Algebra

1838 - 358 σελίδες
...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. From the same formula, we also find nl That is, in any arithmetical progression, the common difference...

## An Introduction to Algebra Upon the Inductive Method of Instruction

Warren Colburn - 1839 - 276 σελίδες
...of the expression, as it is impossible 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 die number of terms less one, to the first term. Example. « What is the 10th term of the series 3,...

## First Lessons in Algebra, Embracing the Elements of the Science ...

Charles Davies - 1839 - 252 σελίδες
...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. From the same formula, we also find n— 1 That is : In any arithmetical progression, the common difference...

## A Practical System of Algebra in Theory and Practice in Two Parts: With a ...

John D. Williams - 1840 - 193 σελίδες
...f4i)=H-^+(a+3rf)==2(a+2rf). 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 is equal to the first term minus that product. Thus, the last...

## An Elementary Treatise on Algebra, in Theory and Practice: With Attempts to ...

John D. Williams - 1840 - 605 σελίδες
...by half the number of terms. And, if the series be decreasing, its sum will be found by subtracting the product of the common difference by the number of terms less one, from twice the first term, and then multiplying the result by half the number of terms, as before.*...

## An Introduction to Algebra, Upon the Inductive Method of Instruction

Warren Colburn - 1841 - 276 σελίδες
...impossible to express the whole until a particular value is given to n. Let I be the term required, then Hence, any term may be found by adding the product...term of the series 3, 5, 7, 9, &c. In this a = 3, •• = 2, and n — 1=9. [na decreasing series, r ie negative. Example. What is the 13th term of...

## Elementary Algebra: Embracing the First Principles of the Science

Charles Davies - 1842 - 258 σελίδες
...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. From the same formula, we also find _ l—a "~n — l' That is : In any arithmetical progression, the...