...anciy — (71 — l]d in a descending one. 137. The sum of all the terms in an arithmetical progression is equal to the sum of the first and last terms multiplied by half the number of terms ; viz. s = ( /"-f- /) ". ( 1 32 Arith.) 2 2d +/+ 3 then Sf+10d = s, «>. (/+/-t-4d)...

...= e-f1z-J-(n — 1J6— sum otjirst and last term, and since S— 2n+(n — l)ix~> it appears that the sum of the series is equal to the sum of the first and last terms for of any two terms equally distant from the first and last terms), multiplied into half the number...

...terms = (a + a+(n— l)6)=sum of first and last term, and since A=(2a+(n— 1)6 -, it appears that the sum of the series is equal to the sum of the first and last terms (or of any t uto termt equally distant from the first and last terms.), multiplied into half the number...

...term y*. The expression to find die length of this series (by theorem 4, p. 72, Simpson's Algebra) is the sum of the first and last terms multiplied by the number of terms, or 7-0710677 + '4044 x 5 • 5 = 41-11507 feet for the total length of the diagonals contained in the...

...term y». The expression to find the length of this series (by theorem 4, p. 73, Simpson's Algebra) is the sum of the first and last terms multiplied by the number of terms, or 7-0710677 + -4041 X 5-5 = 41-11507 feet for the total length of the diagonals contained in the triangle,...

...difference is equal to the difference of the extremes divided by the number of terms minus one. And the sum of the series is equal to the sum of the extremes multiplied by half the number of terms. (1) Given the extremes 12 and 42, and the number of...

...2 a -f- (и — 1) 6f, which is 8 equal to a + z (424.) 1 The sum of the ternis of an equidifferent series is equal to the sum of the first and last terms multiplied by half the number of terms.1 For arranging the series in order, and also in a reverse order, as in the...

...the sum of any number of terms, in such a series, as we know from arithmetic, is equal to the half sum of the first and last terms multiplied by the number of terms ; and any individual term is equal to the product of the common difference into the number of terms...

...difference to or from the preceding ; according as the series is increasing or decreasing. In either case, the sum of the series is equal to the sum of the two extreme terms multiplied by half the number of terms. A series is in Geometrical progression, when...

...consequently, by multiplying by n and dividing by 2, From the first form of this sum, it appears that the sum of the series is equal to the sum of the extremes multiplied by half the number of terms. This equation, like the one in § 131., contains four...