Key to Elements of Algebra : Designed for the use of Canadian Grammar and Common SchoolsContaining Full Solutions to Nearly all the Problems, Together with Numerous Explanatory Remarks . y = sum of 13 terms 9 = {22 + (9 - 1)J] Y = sum of 1 9 terms .-. (ll+(i)3 = (11 + 4,/)9; 11 + d = 33 + 12i .-. Ud = - 23or d = - 2 .-. series is 11, 9, 7, 5, &c. 124. Let m = the m, and n = the n terms of a G. series ;also let a = 1 term, and r = common ratio, then m = ar^-^ aud = /i.»-i n = ar »-l-n + l__«n-?» . J. - I m at - - __r»-l-n + l__«n-» ,_, â , Mi3. Ex. 124-127.] ALGEBRA. 179. m-l\ m - n
Key to Elements of Algebra : Designed for the use of Canadian Grammar and Common SchoolsContaining Full Solutions to Nearly all the Problems, Together with Numerous Explanatory Remarks . y = sum of 13 terms 9 = {22 + (9 - 1)J] Y = sum of 1 9 terms .-. (ll+(i)3 = (11 + 4,/)9; 11 + d = 33 + 12i .-. Ud = - 23or d = - 2 .-. series is 11, 9, 7, 5, &c. 124. Let m = the m, and n = the n terms of a G. series ;also let a = 1 term, and r = common ratio, then m = ar^-^ aud = /i.»-i n = ar »-l-n + l__«n-?» . J. - I m at - - __r»-l-n + l__«n-» ,_, â , Mi3. Ex. 124-127.] ALGEBRA. 179. m-l\ m - n , and common ratio wT-n wh«»re m - the >n^^ and n the n terms of the series. If one of the terms be taken as ihe first, the above becomes 1 125. a= 3; ar* = ^5 .-. r* = i^ .-. r = ± ?. Art. 254, r ^ ~ 22^-3 -I? 2 . ^ ^^ 4 8 16 = 277^ = -W^ â¢â ⢠- ^ y- 9-+27 126. 5â = {2a + (u - l)rf}y ; S^n = {2a + (2/i - l)rf|aand Sgn = {2a + (3/i - l)^}y ^^^° latter half of S-^ = ^^ - S^ = {2a + (2/i - l)r/}« - {2a + (a - l)r/}- 3 nd nd n = an + ânH - y = a/i + (3;t - 1)7- - {2a + (3/i - l)il}y 1 3« = y(2a+(3«-l).i}y 127. Since S^ and ^2 are each to n terms, we haveSy + 8^= 1 + 5 + 9 + &c, to n terms + 3 + 7 + 11 + &c. to ti terms=> 1 + 3 + 5 + 7 + 9 + 11 + &c. to 2n terms = (2n) = 4n^.Also S, - Si = {(1 - 3) + (5 - 7) + (9 - 11) + &c. to n terms}.-. (S - S^y^ = {(1 - 3) + (5 - 7) + &c. to n termsf =( - 2 - 2 - 2- &c. to 71 terms)^ = ( - 2nf = in^ .-. S, + S^ = (i\ - S.^) When S2 = sum to « - 1 termsiSj + ^2 = 1 + 3 + 5 + 7 + &c. to (2Â
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