 | John Bonnycastle - 1811 - 230 páginas
...III. The last term of any arithmetical series is equal to the sum or difference of the first term, and the product of the common difference by the number of terms less , one ; according as the series is increasing or decreasing. Thus, the 20th term of 2, 4, 6, 8, 10, 12, &c.... | |
 | John Bonnycastle - 1813 - 456 páginas
...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. Thus, the... | |
 | John Bonnycastle - 1818 - 326 páginas
...(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. Thus, the... | |
 | Thomas Keith - 1822 - 354 páginas
...13- &c- be 'n arithmetical progression, then will 4. The difference between the extremes is equal to the product of the common difference by the number of terms less one> Thus, if 3. 5. 7. 9. &c. be in arithmetical progression, Tlien will 9—3=2x4—15. The number of terms,... | |
 | James Ryan, Robert Adrain - 1824 - 542 páginas
...rest of the terms. Hence the last term of any arithmetical series is equal to the first term plus or minus, the product of the common difference, by the number of terms less one. 469. Also, if s be put equal to the sum of any number of terms of this progression, we shaU have And... | |
 | James Ryan - 1824 - 550 páginas
...rest of the terms. Hence the last term of any arithmetical series is equal to the. first term plus or minus, the product of the common difference, by the number of terms less one. 469. Also, if s be put equal to the sum of any number of terms of this progression, we shall have And... | |
 | Enoch Lewis - 1824 - 92 páginas
...subsequent term, it is manifest that the whole sum, by which the first term is increased or diminished, is the product of the common difference by the number of terms less one. (48.) The sum of the extremes is evidently equal to the sum of the second from thebeginning, and the... | |
 | John Bonnycastle - 1825 - 336 páginas
...-: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. Thus, the... | |
 | Warren Colburn - 1825 - 400 páginas
...particular value is given to «. Let I be the term required, then Hence,any term may be found by adding the product of the common difference by the number of terms less one, to the first term. Example. What is the 10th term of the series 3, 5, 7, 9, &c. 1 In this a = 3, r... | |
 | Warren Colburn - 1828 - 330 páginas
...to express the whole until a particular value is given to n. Hence, any term may be found by adding the product of the common difference by the number of terms less one, to the first term. Example. What is the 10th term of the series 3, 5, 7, 9, &c. In this a = 3, r =... | |
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That is : The first term of an increasing arithmetical progression is equal to the last term, minus the product of the common difference by the number of terms less one. 
