| Alexander Malcolm - Arithmetic - 1718 - 396 pages
...this Propafition, it follows clearly, that the Sum of all the Terms of an Arithmetical Progreffion, **is equal to the Sum of the Extremes multiplied by half the Number of Terms;** but if that Number is odd, multiply the forefaid Sum, by that whole Number ; and half the Product is... | |
| William Enfield (M.A.) - Amusements - 1821 - 302 pages
...;4 + 8 = 2x6 ^ In the first case, the sum of an arithmetical progression, is equal to the product of **the sum of the extremes multiplied' by half the number of terms;** and in the second, to the product of the mean multiplied by the number of terms. THEOREM III. 23. In... | |
| Nicolas Pike - Arithmetic - 1822 - 536 pages
...equal to the mean (or half the sum of the two extremes) multiplied by the whole number of terms ; or **to the sum of the extremes multiplied by half the number of terms.** The sum of auy number of terms of the arithmetical series of odd numbers 1 , 3, 5, 7, 9, &r.. is equal... | |
| Alexander Ingram - Mathematics - 1830 - 458 pages
...equally distant from it. PROP. III. — The sum of any number of terms in arithmetical progression **is equal to the sum of the extremes multiplied by...number of terms of the series. Cor. 1. — Hence if** * = sum of the series, s = (a+_y)|-. Cor. 2. — If the number of terms be .odd, and m the middle one,... | |
| Bourdon (M., Louis Pierre Marie) - Algebra - 1831 - 326 pages
...finally S. = that is, the sum of the terms of a progression by difference is equal to the product of **the sum of the extremes multiplied by half the number of terms.** If, in this formula, we substitute for I its value a + (n — 1) r, we obtain further o_[2a+ («-l)r]n.... | |
| John Radford Young - Algebra - 1832 - 408 pages
...latter a — (n — l)d. THEOREM 5. The sum of any series of quantities in arithmetical progression **is equal to. the sum' of the extremes multiplied by half the number of terms.** Let a + (a + d) + (a + 2d) + (a + 3d) + &c., be the progression ; then if the number of terms be represented... | |
| Nicolas Pike - Arithmetic - 1832 - 544 pages
...equal tome mean (or half the sum of tiie two extremes) multiplied by the whole numbor of terms ; or **to the sum of the extremes multiplied by half the number of** teruw. The sum of any nmnlfr of terms of the arithmetical series of odd number* 1, 3, 5, 7, 9, ,tc.... | |
| Samuel YOUNG (of Manchester.) - 1833 - 272 pages
...the difference of the extremes divided by the number of terms minus one. And the sum of the series **is equal to the sum of the extremes multiplied by half the number of terms.** (1) Given the extremes 12 and 42, and the number of terms 11. Required the common difference, and sum... | |
| Frederick Emerson - Arithmetic - 1834 - 300 pages
...multiplied by the number of terms and divided by 2; or, which amounts to the same, the sum of all the **terms is equal to the sum of the extremes multiplied by half the** the number of terms. For example, the sum of the following series, 2, 4, 6, 8, 10, 12, 14, 16, is 2... | |
| George Willson - Arithmetic - 1836 - 202 pages
...the reason of this proposition is evident. PROPOSITION III. The sum of all the terms of the series, **is equal to the sum of the extremes multiplied by half the number of terms** ; or, multiplied by the number of terms, and the product divided by 2. For example, 1, 3, 5, 7, 9,... | |
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