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That is, any term is equal to the first term, plus the product of the common difference by the number of preceding terms.
University Algebra: Embracing a Logical Development of the Science: With ... - Page 226
by Charles Davies - 1863 - 311 pages

## A Treatise on Algebra, in Practice and Theory: With Notes and ..., Volume 1

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....

## An Introduction to Algebra: With Notes and Observations : Designed for the ...

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....

## An Introduction to Algebra: With Notes and Observations, Designed for the ...

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....

## Elements of Algebra: Tr. from the French of M. Bourdon. Revised and Adapted ...

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,...

## Elements of Algebra

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...

## An Elementary Treatise on Algebra, Theoretical and Practical: With Attempts ...

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...

## A Practical System of Algebra in Theory and Practice in Two Parts: With a ...

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....

## An Elementary Treatise on Algebra, in Theory and Practice: With Attempts to ...

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....