Question

已知三个数成等差数列,且和为24,此三个数依次加上3,8,21后,即成等比数列,求此等差数列

Answer 1

设此三数分别为：a-d,a,a+d,则

(a-d)+a+(a+d)=24,

(a-d+3)(a+d+21)=(a+8)^2

a=8,

(11-d)(29+d)=16^2

d^2+18d-63=0

(d-3)(d+21)=0

d=3,或d=-21,

等差数列为：5,8,11；或,29,8,-13.