| Andrew Bell (writer on mathematics.) - 1839 - 500 pages
...(и — 1) 6f, which is 8 equal to a + z (424.) 1 The sum of the ternis of an equidifferent series **is equal to the sum of the first and last terms multiplied by half the number of** terms.1 For arranging the series in order, and also in a reverse order, as in the preceding theorem,... | |
| Thomas Tate (mathematical master.) - 1847 - 138 pages
...in the given series. .'. 2s =7x14; .'. s=7J^!! = 49. m This result shows that the sum of the series **is equal to the sum of the first and last terms multiplied by half the number of terms.** In general let it be required to find the sum of the series, s= a + (a + d) + (a + 2d)+ ... to n terms.... | |
| W. Hipsley - Business mathematics - 1852 - 116 pages
...multiplied by one less than the number of terms." " The sum of the terms of an equidifferent series **is equal to the sum of the first and last terms, multiplied by half the number of terms."** First term £20 Last term 20 + 4 44 2^ half the number of terms. 88 22 £110 sum of five terms. As... | |
| W. Hipsley - 1852 - 122 pages
...multiplied by one less than the number of terms." " The sum of the terms of an equidifferent se'ies **is equal to the sum of the first and last terms, multiplied by half the number of terms."** First term £20 Last term 20 + 4 44 : 2^ half the number of terms. 88 22 £110 sum of five terms. As... | |
| William Frederick Greenfield - 1853 - 228 pages
...the sum of two identical series, is twice the sum of one of them. Hence twice the sum of the series **is equal to the sum of the first and last terms multiplied by** the number of terms : or the sum of an Arithmetic series is the sum of the first and last terms multiplied... | |
| James William M'Gauley - 1854 - 284 pages
...is called the greater extreme. EQUIDIFFERENT PROGRESSION. 55. The sum of an equidifferent series h **equal to the sum of the first and last terms, multiplied by half the number of terms.** For, it is equal to all the terms, added together. That is, a, being the lesser extreme ; b, the common... | |
| Noble Heath - 1855 - 468 pages
...of any two corresponding terms of the series. The sum, therefore, of all the terms of both series, **is equal to the sum of the first and last terms multiplied by** the number of terms in one series ; and as this product is evidently just twice the sum of the terms... | |
| Noble Heath - Arithmetic - 1856 - 472 pages
...of any two corresponding terms of the series. The sum, therefore, of all the terms of both series, **is equal to the sum of the first and last terms multiplied by** the number of terms in one series ; and as this product is evidently just twice the sum of the terms... | |
| Barnard Smith - 1857 - 740 pages
...a+b 26. (na-6) + (nl)a+l(-2)« + 6} + &c. to n terms. hence it appears "that the sum of a series in **Arithmetical Progression is equal to the sum of the first and last terms, multiplied** into half the number of terms." Ex. 5. Find the 36"1 term of the series 40, 38, 36, &c., and the sum... | |
| Chambers W. and R., ltd - 1859 - 344 pages
...number of terms 24. Required the lost term, Ans. 13. TlIE SUM OF THE TERMS OF AS EQUIDIFFERENT SERIES **is equal to the sum of the first and last terms multiplied by half the number of terms.** Take any equidifferent series, as 3, 7, 11, 15, 19, 23, consisting of any number of terms, as 6 ; then... | |
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