已知等差数列an的公差为2,若a2,a4,a5成等比数列,则a2的值为?
问题描述:
已知等差数列an的公差为2,若a2,a4,a5成等比数列,则a2的值为?
答
若a2,a4,a5成等比数列,即a4^2=a2*a5
即(a1+3d)^2=(a1+d)(a1+4d),d=2
故(a1+6)^2=(a1+2)(a1+8)
a1^2+12a1+36=a1^2+10a1+16
2a1=-20
a1=-10
a2=a1+d=-10+2=-8