Question

已知等差数列{an}中,若a1+a6=-17,a2*a5=52,且d>0,求a5和an

Answer 1

a1+a6=-17

a1+(a1+5d)=-17

(a1+d)+(a1+4d)=-17

a2+a5=-17

a2×a5=52

因为d>0,所以a5＞a2

由上面方程可解得

a2=-13,a5=-4

a5=a2+3d

-4=-13+3d

3d=9

d=3

an=a1+(n-1)d

=a2+(n-2)d

=-13+3(n-2)

=3n-19