 | William Nicholson - Natural history - 1809 - 684 pages
...1 •* the nlh or last term. • " The sum of a series of quantities in arithmetical progression is found by multiplying the sum of the first and last...term, b the common difference, n the number of terms, and » the sum of the series : Then, _ +<t+'2b...a+n— iT»=s,or, In this case a= 11, 6 = — J, »-'r... | |
 | William Nicholson - 1809 - 716 pages
...-fa — l -u the nlh or last term. " The sum of a series of quantities in arithmetical progression is found by multiplying the sum of the first and last terms by lialf the number of terms." Let a be the first term, 6 the common difference, я the number of terms,... | |
 | William Nicholson - Natural history - 1821 - 378 pages
...+ 71 — 14 the n* or last lerm. " The sum of a series of quantities in arithmetical progression is found by multiplying the sum of the first and last...half the number of terms." Let a be the first term, 4 the common difference, n the number of terms, and » the sum of the series: Then, a +0+4 +qj-24..o+7i... | |
 | William Nicholson - Natural history - 1821 - 376 pages
...n — 1A the «th or last lerm. " The sum of a series of quantities in arithmetical progression is found by multiplying the sum of the first and last...half the number of terms." Let a be the first term, A the common difference, n the number of terms, and a the sum of the series: Then, Sum, 2a+«-lA -|-2a-fn-l... | |
 | Etienne Bézout - Calculus - 1824 - 222 pages
...sum of the terms of this arithmetical progression. But the sum of the terms of such a progression is found by multiplying the sum of the first and last terms by half the number of terms. Whence, this sum will be, (substituting u for its value gt, which is the last term) (S + w) * ~5' Whence,... | |
 | William Whewell - 1837 - 226 pages
...#) = 9« +7.r - 5 a - 5x = 4 a + 2 a: 60. To find the sum of an arithmetical progression, multiply the sum of the first and last terms by half the number of terms. Thus the sum of 10 terms of 1, 3, 5, &C. is (1 + 19) x 5 = 100. For if l + 3 + 5 + &c. to 19 (10 terms)... | |
 | John D. Williams - Algebra - 1840 - 634 pages
...to я terms, we shall have CASE I. The sum of a series of quantities in arithmetical progression is found by multiplying the sum of the first and last terms by half the number of terms. Let a = first term, d = common difference, n = number of terms, and s = sum of the series. a _f- a_j_a _(_... | |
 | John D. Williams - Algebra - 1840 - 216 pages
...to n terms, we shall have CASE I. The sum of a series of quantities in arithmetical progression is found by multiplying the sum of the first and last terms by half the number of terms. Let a = first term, d = common difference, n = number of terms, and s = sum of the series. a + a-\-d + a+2d... | |
 | Augustus De Morgan - Algebra - 1840 - 186 pages
...as before. The rule, then, is : To sum any number of terms of an arithmetical progression, multiply the sum of the first and last terms by half the number of terms. For example, what are 99 terms of the series 1, 2, 3, &c. ? The 99th term is 99, and the sum is (99... | |
 | Thomas Sherwin - Algebra - 1841 - 314 pages
...therefore, ,, n(a S= ^ ' — '-. Hence, M The sum of any number of terms in progression by difference, is found, by multiplying the sum of the first and last terms by half the number of terms, or by multiplying half the sum of the first and last terms by the number of terms. By substituting... | |
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Progression may be found by multiplying the sum of the first and last terms by half the number of terms. 
