...the same in«er. a+4d, a+3«/, a + 2d, a-\-d, a. The sums will be 2a + 4d,2a+4<Z,2a+4d,2a+4d,2a44rf Here we discover the important property, that, 428....last term, of the first but one and the last but one, #c. is 14. And in the other series, the sum of each pair of corresponding terms is 2a+4d. To find the...

...quantities form an ascending geometric series, the sum of the first and last terms is always greater than the sum of any other two terms equally distant from the extremes. 68. Prove that if any quantities, whose differences are inconsiderable with respect to the quantities...

...the first term is the greatest, and the last term the least. In arithmetical progression, the sum of the extremes, is equal to the sum of any other two terms equally distant from the extremes. The sum of the terms is equal to half the sum of the extremes multiplied into the number of terms....

...property, that, 428. In an arithmetical progression, THE SUM OF THE EXTREMES IS EQUAL TO THE SUM OP ANY OTHER TWO TERMS EQUALLY DISTANT FROM THE EXTREMES....series, the sum of each pair of corresponding terms is 2a-[-4d. To find the sum of all the terms in the double series, we have only to observe, that it is...

...obvious from the illustration in Art. 331, that the sum of the extremes in an arithmetical progression, is equal to the sum of any other two terms equally distant from the extremes. Thus, in the series 3, 5, 7, 9, II, the sum of the first and last terms, of the first but one and last...

...a) Hence S=— —= — -. Therefore, PROGRESSIONS. It also appears from the above, that the sum of the extremes is equal to the sum of any other two terms equally distant from the extremes. (238.) The two equations „ at ~2~ ' contain five variable quantities, a, /, d, n, S, of which any...

...the two extremes, multiplied by the number of terms; It also appears from the above, that the sum of the extremes is equal to the sum of any other two terms equally distant from the extremes. (238.) The two equations contain five variable quantities, a, I, d, n, S, of which any three being...

...property, that, 428. In an arithmetical progression, THE SUM OF THE EXTREMES IS EQUAL TO THE SUM OF ANT OTHER TWO TERMS EQUALLY DISTANT FROM THE EXTREMES....series, the sum of each pair of corresponding terms is 2a-f-4d. To find the sum of all the terms in the double series, we have only to observe, that it is...

...Thus, if 9—0=6—3, then will 9 + 3 = 6 + 0. 599. In any arithmetical progression, the sum of the two extremes is equal to the sum of any other two terms equally distant from the extremes, or equal to double the middle term, when the number of terms is odd. Thus, in the series 1, 3, 5,....

...Thus, if 9—6-6—3, then will '9 +3 =6 + 6. 599. In any arithmetical progression, the sum of the two extremes is equal to the sum of any other two terms equally distant from the extremes, or equal to double the middle term, when the number of terms is odd. Thus, in the series 1, 3, 5, 7,...