 That is, any term is equal to the first term, plus the product of the common difference by the number of preceding terms.  Manual of Algebra - Page 245by William Guy Peck - 1875 - 331 pagesFull view - About this book
 | 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+2«i). 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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