 Progression, the sum of the two extremes will equal the sum of any two means equally distant from the extremes ; as 2, 4, 6, 8, 10, 12, The two extremes, 2 + 12 = 6 + 8, the two means.  The Schoolmaster's Assistant: Being a Compendium of Arithmetic, Both ... - Page 103by Thomas Dilworth - 1825 - 194 pagesFull view - About this book
 | Charles Vyse - Arithmetic - 1785 - 350 pages
...Numbers in Arithmetical Progreilion, when the Number of Terms are even, as 1,3,5,7,9,11, or the like, the Sum of the two Extremes will be equal to the Sum of any two Means that are equally diflant from the Extremes ; Vi2. 1,3,5,7,9,11. 2. When the Number of Terms are odd,... | |
 | Charles Vyse - Arithmetic - 1806 - 342 pages
...Arithmetical Progression, when the Number of Terms are even, as 1,3, 5, 7, 9, 11, or the like, the Sum of the two Extremes will be equal to the Sum of any two Means that are equally distant from the Extremes : Viz. 1, 3, 5, 7, 9, 11. 1+11=5+7=3 + 9=12. S: When the... | |
 | James Thompson - Arithmetic - 1808 - 176 pages
...i, . the sum of all the terms. Jfotf — In any series of numbers in Arithmetical Progre«gion, the sum of the two extremes will be equal to the sum of anv two terms equally distant therefrom ¡ as 2, 4, 6, 8, 10, 12 ¡ -where 2+12=14; so 4+10=14; or... | |
 | John Bonnycastle - Algebra - 1813 - 456 pages
...are contained in the following theorems : 1. If four quantities are in arithmetical proportion, the sum of the two extremes will be equal to the sum of the two means. Thus, if the proportionals be 2, 5, 7? 1°? °r и, b, c, d; then will 2 + 10=5 + 7,... | |
 | Daniel Staniford - Arithmetic - 1818 - 332 pages
...extremes ; thus, 5 . 8 . 11 . 14 . 17 .20 ; 5+20=25=8+17=25=11+14=25. 4. If the numbers are odd, the sum of the two extremes will be equal to the sum of any two means equally distant from them, and all be equal to double the odd mean or middle number ; thus, 3.7. 1-1 . 15 . 19 .-23.27;... | |
 | John Bonnycastle - Algebra - 1818 - 326 pages
...are contained in the following theorems : 1. If four quantities are in arithmetical proportion, the sum of the two extremes will be equal to the sum of the two means. Thus, if, the proportionals be 2, 6, 7, 10, or a, b, c, d ; then will 2+M=6+7, and a+d=b+c.... | |
 | Beriah Stevens - Arithmetic - 1822 - 436 pages
...any even number of terms, the sum of the extremes is equal to the sum of the two cciddle terms, or to the sum of any two means equally distant from the extremes. Thus, in the series 3, 5, 7, 9, 11, 13, the sum of 3+13=7+9, or =5+11. The reason is plain : for if... | |
 | Thomas Keith - Arithmetic - 1822 - 354 pages
...progression, then will 5+9=7x2, and 9x5+2x2=7x7. 2. If /OUT numbers be in arithmetical progression, the sum of the two extremes will be equal to the sum of the means. Thus, if •-'. 5. 8. 11. be in arithmetical progression, Then will 2+11=5+8. 3. If a series... | |
 | Zachariah Jess - Arithmetic - 1824 - 224 pages
...; Fifthly, The sum of all the terms. Note. In any series of numbers in arithmetical progression the sum of the two extremes will be equal to the sum of any two terms equally distant therefrom : as," 2, 4, 6, 8, 10, 12; tt,'/(cre2+12 = l4; so 4 + 10= !4; and 6+8=14;... | |
 | John Bonnycastle - Algebra - 1825 - 336 pages
...are contained in the following theorems : 1. If four quantities are in arithmetical proportion, the sum of the two extremes will be equal to the sum of the two means. Thus if the proportionals be 2, 5, 7, 10, or a, b, c, d • then will 2-f 10=5+7, and... | |
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