 | Edward Brooks - 1877 - 438 σελίδες
...the number of terms ; hence we have the following Rule. — The sum of an arithmetical series equals half the sum of the extremes multiplied by the number of terms. 2. The first term equals 3, the last term 65, and number of terms 20 ; required the sum of the terms.... | |
 | Edwin Pliny Seaver, George Augustus Walton - 1882 - 308 σελίδες
...many times as there are terms in the given series, that is n times. Hence or, in words, The sum of all the terms of an arithmetical progression is equal to half the sum of the two extreme terms multi365. The two formulas and S=^(a + l~)n contain all five elements (a, ?, n, d,... | |
 | Daniel W. Fish - 1883 - 364 σελίδες
...plus 1. a + 1 5. s = — 3 — x n. /* The sum of the terms of an arithmetical series is equal to one half the sum of the extremes, multiplied by the number of terms. WRITTEN EXERCISES. 454. 1. The first term of an increasing progression is 8, the common difference... | |
 | Daniel W. Fish - 1883 - 348 σελίδες
...plus 1. a + 1 5. s = — ^ — x n. /^ The sum of the terms of an arithmetical series is equal to one half the sum of the extremes, multiplied by the number of terms. WRITTEN EXERCISES. 454. 1. The first term of an increasing progression is 8, the common difference... | |
 | John Bernard Clarke - 1889 - 566 σελίδες
...the other two. 494.—Theorem. The sum of any number of terms of an arithmetical progression equals half the sum of the extremes, multiplied by the number of terms considered. Let S=af-6+c+d-)- -{-j-\-k-\-tCi), a , b, c, etc., being •whence, adding (1) and (2),... | |
 | Henry Holmes Belfield - 1891 - 362 σελίδες
...series, that is, a-{-l, which, multiplied by ~~2~ V. The sum of the terms of an ascending series equals half the sum of the extremes multiplied by the number of terms; that is, s=( NOTE. A Descending Series may be regarded as an Ascending Series reversed. From the above... | |
 | Edward Brooks - 1895 - 424 σελίδες
...the number of terms; hence we have the following Rule. — The sum of an arithmetical series equals half the sum of the extremes multiplied by the number of terms. WRITTEN EXERCISES. Find the sum 2. Of 12 terms of the series 2, 4, 6, etc. Ans. 156. 3. Of 32 terms... | |
 | George Washington Hull - 1895 - 408 σελίδες
...equals x 8, or 120. From this problem we derive the RULE. The sum of an arithmetical progression equals half the sum of the extremes multiplied by the number of terms. 2. Find the sum of 12 terms of the series 6, 9, 12, etc. PROCESS.— l'2th term = 6 + 11 x3 = 39. Sum... | |
 | Edward Gideon - 1902 - 272 σελίδες
...subtractions. V. The sum of all the terms equals the product of the average value of the terms, or half the sum of the extremes, multiplied by the number of terms. Written Exercises. 447. Example 1. — The first term of a decreasing arithmetical progression is 9,... | |
 | George Soulé - 1910 - 1042 σελίδες
...2, with the same result; hence the Formula, * = ^-~- xn, or, ? xa + I That is, the gum of the aeries is equal to half the sum of the extremes multiplied by the number of terms; or half the number of terms multiplied into the sum of the extremes. 1. The extremes of an arithmetical... | |
| |
That is, the sum of the terms of an arithmetical progression is equal to half the sum of the two extremes multiplied by the number of terms. 
