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" Progression may be found by multiplying the sum of the first and last terms by half the number of terms. "
The elements of algebra - Página 125
por James Wood - 1841 - 305 páginas
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The British Encyclopedia: Or, Dictionary of Arts and Sciences ..., Volumen5

William Nicholson - 1809 - 684 páginas
...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...
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The British encyclopedia, or, Dictionary of arts and sciences, Volumen5

William Nicholson - 1809 - 716 páginas
...-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,...
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British Encyclopedia: Or, Dictionary of Arts and Sciences ..., Volumen10

William Nicholson - 1821 - 378 páginas
...+ 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...
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American Edition of the British Encyclopedia: Or, Dictionary of ..., Volumen10

William Nicholson - 1821 - 376 páginas
...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...
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First Principles of the Differential and Integral Calculus, Or, the ...

Etienne Bézout - 1824 - 222 páginas
...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,...
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The mechanical Euclid, containing the elements of mechanics and hydrostatics

William Whewell - 1837 - 226 páginas
...#) = 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)...
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An Elementary Treatise on Algebra, in Theory and Practice: With Attempts to ...

John D. Williams - 1840 - 634 páginas
...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 _(_...
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A Practical System of Algebra in Theory and Practice in Two Parts: With a ...

John D. Williams - 1840 - 216 páginas
...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...
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The Elements of Arithmetic

Augustus De Morgan - 1840 - 186 páginas
...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...
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An Elementary Treatise on Algebra: For the Use of Students in High Schools ...

Thomas Sherwin - 1841 - 314 páginas
...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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