 | Warren Colburn - 1836 - 286 σελίδες
...impossible to express the whole until a particular value is given to n. Let I be the term required, then Hence, any term may be found by adding the product...series 3, 5, 7, 9, &c. In this a = 3, r = 2, and n — 1 = 9. In a decreasing series, r is negative. Example. What is the 13th term of the series 48,... | |
 | A. Turnbull - 1836 - 368 σελίδες
...above. We have seen, by the last paragraph, that the last term of the series is the first term with the product of the common difference, by the number of terms less one added to it Thus, /+ (» — I) d — I : consequently, if we subtract the first term from the last,... | |
 | Warren Colburn - 1838 - 282 σελίδες
...be found by adding the product of thecommon difference by the number of terms less one, to the iirst term. . . . ' Example. What is the 10th term of the...7, 9>. &c. In this a = 3, r — 2, and n — 1=9. . f / = 3 + 9 X2=21. In a decreasing series, r is negative. Example. What is the 13th term of the series... | |
 | 1838 - 372 σελίδες
...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. From the same formula, we also find nl That is, in any arithmetical progression, the common difference... | |
 | Warren Colburn - 1839 - 308 σελίδες
...of the expression, as it is impossible 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 die number of terms less one, to the first term. Example. « What is the 10th term of the series 3,... | |
 | Charles Davies - 1839 - 264 σελίδες
...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. From the same formula, we also find n— 1 That is : In any arithmetical progression, the common difference... | |
 | John D. Williams - 1840 - 216 σελίδες
...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. Thus, the last... | |
 | John D. Williams - 1840 - 634 σελίδες
...by half the number of terms. And, if the series be decreasing, its sum will be found by subtracting the product of the common difference by the number of terms less one, from twice the first term, and then multiplying the result by half the number of terms, as before.*... | |
 | Warren Colburn - 1841 - 288 σελίδες
...impossible to express the whole until a particular value is given to n. Let I be the term required, then Hence, any term may be found by adding the product...term of the series 3, 5, 7, 9, &c. In this a = 3, •• = 2, and n — 1=9. [na decreasing series, r ie negative. Example. What is the 13th term of... | |
 | Charles Davies - 1842 - 284 σελίδες
...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. From the same formula, we also find _ l—a "~n — l' That is : In any arithmetical progression, the... | |
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The points ..... are used to show that some terms are left out of the expression, as it is impossible to express the whole until a particular value is given to n. 
