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" 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. "
An Introduction to Algebra: Upon the Inductive Method of Instruction - Σελίδα 229
των Warren Colburn - 1837 - 276 σελίδες
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The Elements of Algebra: Designed for Beginners

Elias Loomis - 1862 - 281 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. (205.) If we transpose the term a, and divide by n— 1, we obtain la d= ,; »— 1' that is, in an...

New Elementary Algebra: In which the First Principles of Analysis are ...

Benjamin Greenleaf - 1864 - 324 σελίδες
...as the series is an increasing or a decreasing one. Hence the following RULE. To the first term add the product of the common difference by the number of terms less one. EXAMPLES. 1. If the first term is 5, the common difference 3, and the number of terms 20, what is the...

New Practical Arithmetic in which the Science and Its Applications are ...

Henry Bartlett Maglathlin - 1869 - 324 σελίδες
...the preceding case, the last term ll = 3-)-2 X 4, and subtracting the first term 3, we have 2 X 4, or the product of the common difference by the number of terms less one. Hence, to find the common difference, Divide the difference of the extremes by the number of terms...

Elementary Algegra

Daniel Barnard Hagar - 1873 - 263 σελίδες
...Means. Theorem I. 346. The last term of an arithmetical progression is equal to the first term plus the product of the common difference by the number of terms less one. Let the terms of the progression be a, a+d, a+2d, a+3d, . . . The coefficient of d in the last term...

New Practical Arithmetic: In which the Science and Its Applications are ...

Henry Bartlett Maglathlin - 1873 - 336 σελίδες
...the preceding case, the last term llr=3-)-2 X 4, and subtracting the first term 3, we have 2 X 4, or the product of the common difference by the number of terms less one. Hence, to find the common difference, Divide the difference of the extremes by the number of terms...

The Complete Arithmetic, Oral and Written: Second Part

Daniel W. Fish - 1874 - 272 σελίδες
...number of terms 9 ; what is the first term ? EULE. — I. If the given extreme is the less, add to it the product of the common difference by the number of terms less one. II. If the given extreme is the greater, subtract from it the product of the common difference by the...

The Complete Arithmetic: Oral and Written

Daniel W. Fish - 1874 - 516 σελίδες
...OPERATION. ANALYSIS.—The difference between •^Qg g . 19 — 5 — t£ the extremes is equal to the product of the common difference by the number of terms less one (829); hence the common difference is ff, or 5. 2. The extremes of a progression are 1 and 17, and...

The Progressive Higher Arithmetic: For Schools, Academies, and Mercantile ...

Horatio Nelson Robinson - 1875 - 456 σελίδες
...the common difference ; and so on. In all cases the difference between the two extremes is equal to the product of the common difference by the number of terms less 1. Hence the RULE. Multiply the common difference by the number of terms less 1 , add the product to...

The Philosophy of Arithmetic as Developed from the Three Fundamental ...

Edward Brooks - 1876 - 570 σελίδες
...plus twice the common difference, etc. ; hence we infer that the last term equals the first term plus the product of the common difference by the number of terms less one. In finding the sum of the terms we take a series, then write under this series the same series in an...

The New American Arithmetic, Μέρος 3

Samuel Mecutchen, George Mornton Sayre - 1877
...term is therefore equal to 27 less than the first, or 29 — 27 = 2. RULE. To the less extreme add the product of the common difference by the number of terms less one; or, subtract this product from the greater extreme; the result in either case will be the other extreme....




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