Question Number 101779 by I want to learn more last updated on 04/Jul/20

If    S_n   is the sum of the first  n  terms of an A.P.  Express   S_(2k)   in terms of   S_k   and   S_(3k)

Answered by bemath last updated on 04/Jul/20

S_n  = ((n(a+u_n ))/2)→ S_(k ) = ((k(a+u_k ))/2)  u_k = ((2S_k )/k)−a ⇒a+(k−1)d=((2S_k )/k)−a  (k−1)d = ((2S_k )/k)−2a⇒d =((2S_k −2ak)/(k(k−1))) (•)  S_(2k)  = ((2k(a+u_(2k) ))/2) = k(a+u_(2k) )  u_(2k)  = (S_(2k) /k)−a ⇔a+(2k−1)d=(S_(2k) /k)−a   d = ((S_(2k) −ak)/(k(2k−1))) (••)  (•)=(••)  ((2S_k −2ak)/(k(k−1))) = ((S_(2k) −ak)/(k(2k−1)))  ⇒(((2k−1)(2S_k −2ak))/(k−1)) +ak = S_(2k)

Commented byI want to learn more last updated on 05/Jul/20

Thanks sir. I appreciate