 | Alexander Malcolm - 1718 - Liczba stron: 396
...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 - Liczba stron: 304
...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... | |
 | 1817 - Liczba stron: 214
...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, the... | |
 | William Enfield (M.A.) - 1821 - Liczba stron: 302
...difference taken as many times as there are terms, before it. (22.) 2nd. The sum of the extremes is always equal to the sum of any two terms equally distant from them ; or double the mean term, if the progression contains an odd number of terms. (21.) 3rd. If the sum... | |
 | Stephen Pike - 1824 - Liczba stron: 212
...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 double... | |
 | Ferdinand Rudolph Hassler - 1826 - Liczba stron: 224
...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 equally distant from them, for the sum of every such pair of terms must contain the first term twice, and the constant difference... | |
 | James L. Connolly (mathematician.) - 1829 - Liczba stron: 266
...last terms are called the extremes. In a series of even numbers, the sum of the two extremes will be equal to the sum of any two terms, equally distant from them; as 2, 4, 6, 8, 10, the two extremes beinj* 2+10=12,804+8=12; but if the number of terms be odd, the... | |
 | Alexander Ingram - 1830 - Liczba stron: 458
...y — d, y ; where the sum of any two corresponding terms is a-\-y. Cor. — The double of any term is equal to the sum of any two terms equally distant from it. PROP. III. — The sum of any number of terms in arithmetical progression is equal to the sum of... | |
 | Martin Ruter - 1831 - Liczba stron: 190
...&,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, in... | |
 | 1831 - Liczba stron: 210
...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 i! the latter of the above series 6+1=4+3, and =5+2. i When the number of terms is odd, the double... | |
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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. 
