 | Alexander Malcolm - 1718 - 396 pages
...Remainder is the other middle Term. Profofition 3d, IN an Arithmetical Progrejjion, (V. Definition 5th) the Sum of the Extremes is equal to the Sum of any two Terms, at equal Diilance from them ; or to double the middle Term (if the Number of Terms are odd; ) confequently... | |
 | Jeremiah Day - 1814 - 304 pages
...The sums will be Here we discover the important property, that, 428. In an arithmetical progression, the sum of the extremes is equal to the sum of any other two terms equally distant from the extremes. In the series of numbers above, the sum of the first... | |
 | John Dougall - 1815 - 514 pages
...extremes, and the 2nd and 3rd the means. The fondamental property of numbers in arithmetical proportion is that the sum of the extremes is equal to the sum of the means ! tims in 5, 10, 8, 13, the sum of the extremes § and 13, or 18, is equal to the sum of... | |
 | 1817 - 214 pages
...called the extremes. JVote. — In any series of numbers in arithmetical progression, the sum of the two extremes is equal to the sum of any two terms equally distant from them ; as in the latter of the above series 6-fl=4-f-3, and=5-{-2. Whei. the number of terms is odd,... | |
 | Stephen Pike - 1824 - 212 pages
...called the extremes. Note. — In any series of numbers in arithmetical progression, the sum of the two extremes is equal to the sum of any two terms equally distant from them; as in the latter of the above series 6 + 1=4+3, and =5+2. When the number of terms is odd, the... | |
 | Bézout - 1825 - 258 pages
...PROPERTIES OF ARITHMETICAL PROPORTION. 176. The fundamental property of arithmetical proportion, is that the sum of -the extremes is equal to the sum of the •means : for example, in this proportion 3.7:8.12, the sum 3 and 12 of the extremes, and that... | |
 | Ferdinand Rudolph Hassler - 1826 - 224 pages
...deduced from the nature of the series, in the following manner. As we found in arithmetic proportion that the sum of the extremes is equal to the sum of the means, so it is evident that here the sum of the extremes is equal to the sum of any two terms... | |
 | Alexander Ingram - 1830 - 458 pages
...the nth term is n — 1. Cor. — Hence y = a + (n — l)d, and a =y — (n — l)d. PROP. II. — The sum of the extremes is equal to the sum of any two terms equally distant from them. For any term exceeds the least, as much as its corresponding term is less than the greatest.... | |
 | Martin Ruter - 1831 - 190 pages
...&,c. — the common dil ference is 3. In any series in Arithmetical Progression, the sum o the two extremes is equal to the sum of any two terms equally distant from them, or equal to double the mid die term when there is an uneven number o£ terms i lie series. Thus,... | |
 | Thomas Conkling (W.) - 1831 - 302 pages
...half the number of terms. * In any series of numbers, in arithmetical progression, the sum of the two extremes is equal to the sum of any two terms equally distant from then}; as in the series above, 2 +• 10, is equal to 4 +• 8, &c. : ' When the number of terms is... | |
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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. 
