解:
27. 一等差數列a1, 42, ……, “100,已知470-457<0,那麼下列哪一個選項是正確的?
(A)a43-a69>0
(B)a42-a51 <0
(C)a18+a51a21+A48
(D)a12+a31a9+a34
a70
-
a57 =
(a₁ +69d) (a₁ +56d) = 13d <0⇒d<0
(A)a43 - a69 = (a₁ +42d) − (a₁ +68d) =-26d>0⇒a43 > a69
=
-
(B)a42 a51 =
= (a₁ +41d) — (a₁ +50d) = −9d > 0 ⇒ A42 > A51
(C)a18 + a51
-
(a₁ + 17d) + (a₁ +50d) = (a₁ +20d) + (a₁ +47d) = a21 + a48
(D)a12 + a31 = (a₁ + 11d) + (a₁ + 30d) = (a₁ + 8d) + (a₁ +33d) = ag + a33
故選(A)
