 | Samuel Alsop - 1857 - 150 pages
...represent four such quantities, then : b — a = d — c, when by transposition 6 -f- c = a -(- d. § 111. The sum. of the extremes is equal to the sum of any two terms equally distant from them. Let a, a -f- d, a -f- % d, &c. be the series commencing with the least. IfZbe the last terra,... | |
 | James Stewart Eaton - Arithmetic - 1857 - 376 pages
...the third is as much greater than the first as the last but two is less than the last ; etc. ; .-. the sum of the extremes is equal to the sum of any other two terms which are equally distant from the extremes ; thus, in the series 1, 4, 7, 10, 13,... | |
 | James Wharton - 1860 - 176 pages
...mean between 2 and 7 ; and shew that the sum of the first and last terms of an arithmetical series is equal to the sum of any two terms equally distant from the first and last terms respectively. (12.) If a : b : : с : d : : e :/, shew that ,. , a + b _ с +... | |
 | James Stewart Eaton - 1862 - 320 pages
...terms ? 372. PROBLEM 4. To find the sum of a series, the extremes and number of terms being given. The sum of the extremes is equal to the sum of any two terms that are equally distant from the extremes; thus, in the series, 3, 5, 7, 9, 11, 18, we have 8 + 18... | |
 | James Stewart Eaton - Arithmetic - 1864 - 322 pages
...8, Ana. 372. PROBLEM 4. To find the sum of a series, the extremes and number of terms being given. The sum of the extremes is equal to the sum of any two terms that are equally distant from the extremes ; thus, iu the series, 3, 5, 7, 9, 11, 13, we have 1st 4-... | |
 | James Wharton - 1864 - 180 pages
...harmonical mean between 2 and 7; and shew that the sum of the first and last terms of an arithmetical series is equal to the sum of any two terms equally distant from the first and last terms respectively. (12.) If а : 4 : : о : <Z : : e :/, shew that ,. , a + 6 c + d... | |
 | Joseph Ray - Algebra - 1866 - 252 pages
...— Multiply half the sum of the two extremes by the number of terms. From the preceding, it appears that the sum of the extremes is equal to the sum of any other two terms equally distant from the extremes. Since l=a-\-(n — l)<Z, if we substitute this in... | |
 | Joseph Ray - Algebra - 1866 - 250 pages
...— Multiply half the sum of the two extremes by the number of terms. From the preceding, it appears that the sum of the extremes is equal to the sum of any other two terms equally distant from the extremes. Since l=a-\-(n — 1)J, if we substitute this in... | |
 | Horatio Nelson Robinson - Algebra - 1866 - 328 pages
...sum of its terms must be twice that of the given series. Heuce, in an arithmetical progression, I. The sum of the extremes is equal to the sum of any other two terms equally distant from the extremes. II Twice the sum of the series is equal to the sum... | |
 | Ezra S. Winslow - Business mathematics - 1867 - 232 pages
...less extreme. The numbers between these, (9, 7, 5,) are the means. In every arithmetical progression, the sum of the extremes is equal to the sum of any two means that are equally distant from the extremes; and is, therefore, equal to twice the middle term,... | |
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And we may moreover observe, that the sum of the extremes is equal to the sum of any two terms equally distant from the extremes, or to twice the middle term, when the number of terms is odd. 
