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