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" Divide the difference of the extremes by the common difference, and the quotient increased by 1 is the number of terms. "
The New Complete System of Arithmetick: Composed for the Use of the Citizens ... - Page 241
by Nicolas Pike - 1807 - 352 pages
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Introduction to the National Arithmetic: On the Inductive System Combining ...

Benjamin Greenleaf - Arithmetic - 1859 - 334 pages
...of the extremes, and the product divided by 2, the quotient will be the sum of the series. Hence the RULE. — Divide the difference of the extremes by the common difference, and to the quotient add 1 ; multiply this sum by the sum of the extremes, and half the product is the sum...
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Higher Arithmetic : Or, The Science and Application of Numbers: Combining ...

James Bates Thomson - Arithmetic - 1860 - 440 pages
...common difference ? 605. To find the number of terms, when the extremes and common difference are given. Divide the difference of the extremes by the common difference, and the quotient increased by 1 will be the number of terms. OBS. The truth, of this principle is manifest from the...
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The National Arithmetic, on the Inductive System: Combining the Analytic and ...

Benjamin Greenleaf - Arithmetic - 1860 - 460 pages
...divided by 2, the quotient will be the sum of the series; therefore 19^"8 X 9 = 99, the answer required. RULE. — Divide the difference of the extremes by the common difference, and to the quotient add I ; by this sum multiply half the sum of the extremes, and the product will be...
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Bryant and Stratton's Commercial Arithmetic: In Two Parts. Designed for the ...

Emerson Elbridge White - Arithmetic (Commercial), 1861 - 1861 - 348 pages
...number of terms, less one. (3). The first term, common difference, and last term being given to find the number of terms. RULE. — Divide the difference of the extremes by the common difference, and add 1 to the quotient. (4). The first term, number of terms, and last term being given to find the...
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Introduction to the National Arithmetic, on the Inductive System: Combining ...

Benjamin Greenleaf - Arithmetic - 1861 - 338 pages
...of differences; therefore, 9 -f- 1 = 10 is the number of terms in this series. Hence the following RULE. — Divide the difference of the extremes by the common difference, and the quotient. increased by 1, will be the number of termi required. EXAMPLES FOR PRACTICE. 1. If the extremes of...
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The Common School Arithmetic: Combining Analysis and Synthesis; Adapted to ...

James Stewart Eaton - 1862 - 320 pages
...extremes is the common difference multiplied by one less than the number of terms. Hence, conversely, RULE. Divide the difference of the extremes by the common difference, and the quotient, increased by 1, is the number of terms. Ex. 1. The extremes of an arithmetical series are 3 and 31...
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The Common School Arithmetic: Combining Analysis and Synthesis ; Adapted to ...

James Stewart Eaton - Arithmetic - 1864 - 322 pages
...is the common difference multiplied by one less than the number of terms. Hence, conversely, R0LE. Divide the difference of the extremes by the common difference, and the quotient, increased by 1, is the number of terms. Ex. 1. The extremes of an arithmetical series are 3 and 31...
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The parallel arithmetic

W H. Wingate - 1865 - 150 pages
...extremes by one less than the number of terms. . 3. The extremes and difference being given, to find the number of terms. Rule. — Divide the difference of the extremes by the common difference of the series ; to the quotient add one for the answer. 4. The last term, number of terms, and common...
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The Common School Arithmetic: Combining Analysis and Synthesis, Adapted to ...

James Stewart Eaton - Arithmetic - 1866 - 328 pages
...extremes is the common difference multiplied by one less than the number of terms. Hence, conversely, RULE. Divide the difference of the extremes by the common difference, and the quotient, increased by 1, is the number of terms. Ex. 1. The extremes of an arithmetical series are 3 and 31...
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The Common School Arithmetic: Combining Analysis and Synthesis; Adapted to ...

James Stewart Eaton - Arithmetic - 1867 - 358 pages
...is the common difference multiplied by one less than the number of terms. Hence, conversely, RULF.. Divide the difference of the extremes by the common difference, and the quotient, increased by 1, is the number of terms. Ex. 1. The extremes of an arithmetical series are 3 and 31...
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