 | William Smyth - Algebra - 1830 - 278 pages
...so also c — 6 = k — h whence c -J- h= from which we infer that in a progression by difference, the sum of any two terms taken at equal distances from the extremes is equal to the sum of the extremes. Let S represent the sum of all the terms in the progression... | |
 | Bourdon (M., Louis Pierre Marie) - Algebra - 1831 - 446 pages
...x=a+pXr, and y=l—pxr; whence, by addition, x+y=a + l. which demonstrates that, in any progression, the sum of any two terms, taken at equal distances from the two extremes, is equal to ihesum of these extremes, or the two extremes and any two terms taken at equal distances... | |
 | Bourdon (M., Louis Pierre Marie) - Algebra - 1831 - 326 pages
...= 1 — p X r; whence we deduce, by adding x + y = « + i; which shows, that in every progression, the sum of any two terms, taken at equal distances from the extremes, is equal to the sum of the extremes ; or the two extremes, and two terms taken at equal distances... | |
 | Charles Davies - Algebra - 1835 - 378 pages
...number of terms less one. 217. A progression by differences being given, it is proposed to prove that, the sum of any two terms, taken at equal distances from the two extremes, is equal to the sum of the two extremes. Let abcdef...ikl, be the proposed progression, and n the number... | |
 | Benjamin Peirce - Algebra - 1837 - 300 pages
...is, the mth term counting from the last of the given series, is 177. Corollary. The sum of the mth term and of the mth term from the last is, therefore,...arithmetical series, is equal to the sum of the two extremes. 178. Problem. To find the sum of an arithmetical progression when its first term, last term, and number... | |
 | Benjamin Peirce - Algebra - 1837 - 300 pages
...of the mlh term and of the mth term from the last is, therefore, [a + (m_l)r] + [/_(m—l)r]=a + /; that is, the sum of any two terms, taken at equal...arithmetical series, is equal to the sum of the two extremes. • 178. Problem. To find the sum of an arithmetical progression when its first term, last term, and... | |
 | Benjamin Peirce - Algebra - 1837 - 302 pages
...mth term and of the mth term from the last is, therefore, [a + (,„ _ l)r] + [/— (m- l)r] = a + I; that is, the sum of any two terms, taken at equal...arithmetical series, is equal to the sum of the two extremes. 178. Problem. To find the sum of an arithmetical progression when its first term, last term, and number... | |
 | Algebra - 1838 - 372 pages
...the last term ? Ans. 22. 164. A progression by differences being given, it is proposed to prove that, the sum of any two terms, taken at equal distances from the two extremes, is equal to the sum of the two extremes. Let a .b . c . d . e .f . . . . 1 . £ . Z be the proposed... | |
 | Charles Davies - Algebra - 1839 - 272 pages
...last term ? Ans. 402. 14O. A progression by differences being given, it is proposed to prove that; the sum of any two terms, taken at equal distances from the two extremes, is equal to the sum of the two extremes. That is, if we have the progression 2 . 4 . 6 . 8 . 10 . 12,... | |
 | Charles Davies - Algebra - 1842 - 284 pages
...last term ? Ans. 402. 14O. A progression by differences being given, it is proposed to prove that, the sum of any two terms, taken at equal distances from the two extremes, is equal to the sum of the two extremes. That is, if we have the progression 2 . 4 . 6 . 8 . 10 . 12,... | |
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... which the first term is /, and the common difference — r. Hence the mth term of this series, that is, the mth term counting from the last of the given series, is /_(,„_ 1 ) r . 248. 
