 It will be observed that the exponent of r in any term is one less than the number of the term. Hence, in the nth or last term, the exponent of r will be n — 1.  College Algebra - Page 157by Charles Hamilton Ashton, Walter Randall Marsh - 1907 - 279 pagesFull view - About this book
 | James Maginness - Arithmetic - 1821 - 378 pages
...sum of all the terms. Then the series will be a, or, arz, ar3, ar* ---- z. And since it appears that the exponent of r, in any term, is one less than the number expressing the place of that term, it is evident, that z — arn~~ • Now, s=a+ar+ar3 + ar* ---- +arn~"Therefore,... | |
 | Horatio Nelson Robinson - Algebra - 1846 - 276 pages
...power in the 3d term, the third power in the 4th term, and thus universally, the power of the ratio in any term is one less than the number of the term. The first term is a factor in every term. Hence the 10th term of this general series is or9. The 17th... | |
 | John Bonnycastle - 1848 - 334 pages
...of the series, then we shall have , — a + or + ar' + ar3 + ar4 + ..... + ai*-' + where the index of r in any term is one less than the number of the term ; hence we have (1) Again, s = a + ar + ar' + ar3 + .... + ar--2 + ar»-i, .-. rs = ar + ar2 + ar3... | |
 | Horatio Nelson Robinson - Algebra - 1848 - 354 pages
...power in the 3d term, the third power in the 4th term, and thus universally the power of the ratio in any term is one less than the number of the term. The first term is a factor in every term. Hence the 10th term of this general series is ar^. The 17th... | |
 | Horatio Nelson Robinson - Algebra - 1850 - 256 pages
...third term, the third power of r in the fourth term, and thus, universally, the power of the ratio in any term, is one less than the number of the term. The first term is a factor in every term. Hence, the 10th term of this general series is ar9. The 1... | |
 | Horatio Nelson Robinson - Arithmetic - 1859 - 362 pages
...three times, or its third power, we have the fourth term ; and, in general, the power of the ratio in any term is one less than the number of the term. The ascending series, 2, 6, 18, 54, may be analyzed thus : 2, 2 X 3, 2 X 3X3, 2X3X3X3. In this illustration... | |
 | Horatio Nelson Robinson - Algebra - 1866 - 328 pages
...series. And we observe, Ist. The first term, a, is taken once in every term. 2d, The coefficient of d in any term is one less than the number of the term counted from the left. Therefore the tenth te:m would be expressed by a + Qd; The 17th term by a +... | |
 | Adolf Sonnenschein - 1870 - 276 pages
...term, &c. a, a + d, a + 2 xd, a + 3 xd, a + 4 xd, &c., where the number of d! s added to a in each term is one less than the number of the term ; thus the 20th term will be a + 1 9 xd, and the 1000th term of the above series is 1 + 999 x 2£ = 2623-jj-.... | |
 | Edward Olney - Algebra - 1873 - 354 pages
...number of the term less 1, ie, for the nth term, m— (n — 1), or m — n+ 1 ; and the exponent of y in any term is one less than the number of the term, ie, for the nth tenu, n — \. 170. DEF. — In a series the Scale of Relation is the relation which... | |
 | Horatio Nelson Robinson - Algebra - 1874 - 340 pages
...series. And we observe, ls<. The first term, a, is taken once in every term. 2d. The coefficient of d in any term is one less than the number of the term counted from the left. Therefore the tenth term would be expressed by a + 9d; The 17th term by a +... | |
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