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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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The National Arithmetic, on the Inductive System

Benjamin Greenleaf - Arithmetic - 1847 - 336 pages
...miles, 2 rods. PROBLEM III. Given the extremes and the common difference, to find the number of terms. 1 RULE. Divide the difference of the extremes by the common difference, and the quotient increased by one, will be the number of terms required 9. Tf the extremes are 3 and 45, and the common...
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Welch's Improved American Arithmetic, Adapted to the Currency of the United ...

Arithmetic - 1847 - 292 pages
...the first term, the last term, and the common difference, tojind the number of terms. RULE. — 0) Divide the difference of the extremes by the common difference, and the quotient increased by one is the number of terms required. Question. — 1. The first and last terms, and common...
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Higher Arithmetic: Or, The Science and Application of Numbers; Combining the ...

James Bates Thomson - Arithmetic - 1847 - 434 pages
...common difference ? 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. Tlie truth of this principle is manifest from the...
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Higher Arithmetic; Or, The Science and Application of Numbers: Combining the ...

James Bates Thomson - Arithmetic - 1848 - 434 pages
...common difference ? GO5. 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 Elements of Arithmetic...: In which Decimal and Integral ..., Part 2

Pliny Earle Chase - Arithmetic - 1848 - 244 pages
...5, gives 7, which must be equal to the number of terms less 1. Therefore the number of terms is 8. RULE. Divide the difference of the extremes by the common difference, and add 1 to the quotient. 13. What is the sum of the series 2, 4, 6, 8, &c., to 1000? 14. What is the...
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Daboll's Complete Schoolmaster's Assistant: Being a Plain Comprehensive ...

Nathan Daboll, David Austin Daboll - Arithmetic - 1849 - 260 pages
...and the number of terms 140.) CASE IV. The first term, last term and common difference given, to Jind the number of terms. RULE. Divide the difference of...extremes by the common difference, and the quotient increased by 1, will be the number of terms. EXAMPLES. 1 . A man bought cloth in arithmetical progression,...
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Scribner's Engineers' and Mechanics' Companion: Comprising United States ...

J. M. Scribner - Mechanical engineering - 1849 - 286 pages
...common difference. 29-3=26 ; and 26-M3=2. Ans. Gicen the Common Difference and the Extremes, to find the Number of Terms. Rule. — Divide the difference of the extremes by the common difference, and to the quotient add one. Example. — The first term of an arithmetical progression is 11, the last...
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Higher Arithmetic: Designed for the Use of High Schools, Academies, and ...

George Roberts Perkins - Arithmetic - 1849 - 344 pages
...the first term, the last term, and the common difference, to find the number of terms, we have this RULE. Divide the difference of the extremes by the common difference, and to the quotient add one. EXAMPLES. 1. The first term of an arithmetical progression is 5, the last...
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Introduction to The National Arithmetic: On the Inductive System Combining ...

Benjamin Greenleaf - Arithmetic - 1849 - 336 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 add 1 to the quotient ; multiply this sum by the sum of the extremes, and half the product is the sum...
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A New System of Arithmetic on an Improved Plan

Charles Guilford Burnham - 1850 - 350 pages
...Therefore — Art. 239. — When the first and last terms, and the common difference are given, to find the number of terms — RULE. Divide the difference...extremes by the common difference, and the quotient will be 1 less than the number of terms. 10. If the first term of a series be 2, and the last term...
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