Question

在-1與7之間順次插入三個(gè)數(shù)a、b、c,使這5個(gè)數(shù)成等差數(shù)列，則這個(gè)數(shù)列為__________.

Answer 1

解析:法一:設(shè)這5個(gè)數(shù)組成的等差數(shù)列為{a_n},由已知a₁=-1,a₅=7,7=-1+(5-1)d.故d=2,從而這個(gè)數(shù)列為-1,1,3,5,7.

法二:∵-1,a,b,c,7成等差數(shù)列,∴b是-1與７的等差中項(xiàng),a是-1與b的等差中項(xiàng),c是b與７的等差中項(xiàng),即b==3,a==1,c==5.

∴所求數(shù)列為-1,1,3,5,7.

答案:-1,1,3,5,7