| John Bonnycastle - Algebra - 1813 - 456 pages
...+ (a + 4d) — a + d+ (a + 3d) = 2 x (a+2d). 5. The last term of any increasing arithmetical series **is equal to the first term plus the product of the common difference by the number of** terms less one ; and if the series be decreasing, it will he equal to the first term minus that product.... | |
| John Bonnycastle - Algebra - 1818 - 326 pages
...then will a+(a+4d)=(a+d)+(a+3d)=2 X(o+2Ģi). 5. The last term of any increasing arithmetical series **is equal to the first term plus the product of the common difference by the number of** terms less one ; and if the series be decreasing, it will be equal to the first term minus that product.... | |
| John Bonnycastle - Algebra - 1825 - 336 pages
...o + (o + 4d) = (o + d) + ,a+ -:d)= x (a+td.) 5. The last term of any increasing arithmetical series **is equal to the first term plus the product of the common difference by the number of** terms less one ; and it ^ the series be decreasing, it will be equal to the first term minus that product.... | |
| Charles Davies - Algebra - 1835 - 378 pages
...which marks the place of it, the expression for this general term, is l=a+(n—l)r. That is, the last **term is equal to the first term, plus the product of the common difference by the number of** terms less one. If we suppose n successively equal to 1, 2, 3, 4, &c. we shall obtain the first, second,... | |
| Algebra - 1838 - 372 pages
...which marks the place of it, the expression for this general term, is l=a+(n— l)r. That is, the last **term is equal to the first term, plus the product of the common difference by the number of** terms less one. If we make n=l, we have l=za ; that is, the series will have but one term. If we make... | |
| John Radford Young - 1839 - 332 pages
...also when the series is decreasing. THEOREM 4. In any increasing arithmetical progression, the last **term is equal to the first term plus the product of the common difference** and number of terms less one ; but if the progression be decreasing, then the last term is equal to... | |
| John D. Williams - Algebra - 1840 - 216 pages
...then will a+ (a f4i)=H-^+(a+3rf)==2(a+2rf). 5. The last term of any increasing arithmetical series **is equal to the first term plus the product of the common difference by the number of** terms less one ; and if the series be decreasing, it is equal to the first term minus that product.... | |
| John D. Williams - Algebra - 1840 - 634 pages
...senes be a, a-\-d, a+2d, a+3d, a + 4d, then will 5. The last term of any increasing arithmetical series **is equal to the first term plus the product of the common difference by the number of** terms less one ; and if the series be decreasing, it is equal to the first term minus that product.... | |
| Charles Davies - Algebra - 1842 - 368 pages
...it, the expression for this general term, is l=a+(nl)r. That is, the last term is equal to the Jirst **term, plus the product of the common difference by the number of** terms less one. If we make n—1, we have I—a; that is, the series will have but one term. If we... | |
| Charles Davies - Algebra - 1845 - 382 pages
...terms will be denoted by n — 1, and the expression for this general term, will be I = a + (n — l)d. **That is, any term is equal to the first term, plus...common difference by the number of preceding terms.** If we make n = 1, we have / = a ; that is, the series will have but one term. If we make n = 2, we... | |
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