 | Daniel Leach - Arithmetic - 1851 - 280 pages
...are five things to be considered — the first term, the last term, the number of terms, the ratio, and the sum of all the terms. When any three of them are known, the other two may easily be found. OBS. 1. The product of the extremes of any series is equal... | |
 | Oliver Byrne - Engineering - 1852 - 600 pages
......... inverted, 15 , 13 , 11 , _ 9, 7, 5, 3^ _ 1; the sums are, 16 + 16 + 16 + 16 + 16 + 16 + 16 + 167 which must be double the sum of the single series,...three of them are given, as in the following Problems : PROBLEM I. Given the extremes and tlie number of terms, to find the gum of all the terms. RULE. —... | |
 | Daniel Leach - Arithmetic - 1853 - 622 pages
...are five things to be considered — -the first term, the last term, the number of terms, the ratio, and the sum of all the terms.. When any three of them are known, the other two may easily be found. Ofs. 1. The product of the extremes of any series is equal... | |
 | Charles Haynes Haswell - Engineering - 1853 - 318 pages
...parts are given, the remaining two can be found, viz. : The First term, the Last term, the Number oi terms, the COMMON DIFFERENCE, and the SUM of all the terms. When the First- Term, the Common Difference, and the Number of Terms are given, to find the Last Term. RULE.... | |
 | C W. Thornhill - 1854 - 228 pages
...order it will explain the reason. 123456 654321 777777 These theorems will enable the pupil to find any one of these five parts ; the two extremes, the...the common difference, and the sum of all the terms. If any three of these be given the other two may be found. CASE 1. — The extremes and the number... | |
 | Thomas Tucker Smiley - Arithmetic - 1854 - 192 pages
...five things to be particularly attended to in Arithmetical Progression; the first term, the last term, the number of terms, the common difference, and the sum of all the terms. Case 1. The first term, common difference, and number of terms, being given, to find the last term,... | |
 | David Price - Arithmetic - 1858 - 264 pages
...difference. There are five particulars that claim especial attention ; viz, the first term, the last term, the number of terms, the common difference, and the sum of all the terms. 3, 6, 9, 12 is an ascending series, of which 3 is the first term, 12 is the last term, the number of... | |
 | James Bates Thomson - Arithmetic - 1860 - 440 pages
...arithmetical progression there are five parts to be considered, viz : the first term, t/ie last term, the number of terms, the common difference, and the sum of all tfte terms. These parts have such a relation to each other, that if any three of them are given, the... | |
 | Oliver Byrne - Engineering - 1863 - 600 pages
......... inverted, 15 , 13 , 11 , 9 , 7 , 5 , 3 , 1 ; the sums are, 16 + 16 + 16 + 16 + 16 + 16 + 16^Fl67 which must be double the sum of the single series,...three of them are given, as in the following Problems : PROBLEM I. Given the extremes and the number of terms, to find the sum of all the terms. RULE. —... | |
 | Thomas Tucker Smiley - 1868 - 238 pages
...five things to be particularly attended to in Arithmetical Progression; the first term, the lust term, the number of terms, the common difference, and the sum of all the terms. Case 1. The first term, common difference, and number of terme, being given, to find the last term,... | |
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From these theorems may readily be found any one of these five parts ; the two extremes, the number of terms, the common difference, and the sum of all the terms, when any three of them are given, as in the following Problems : PROBLEM I. 
