12000-1500X=12000*5%+(12000-1500)5%+(12000-1500*2)*5%+...+[12000-1500(x-1)]*5%
12000-1500X=12000*5%*X-5%*1500*[1+2+3+...+(X-1)]
X=5.2 The debt will be paid off in 6 years.
2.Suppose the equal ratio as q,the sequence will be 2/q,2,2q,2q^2,the sum of which:
2/q+2+2q+2q^2=8
q^3+q^2-3q+1=0
q^2(1-q)+q(1-q)+(1-q)=0
(q^2+q+1)(1-q)=0
for q^2+q+1=(q+1/2)^2+3/4>0,1-q=0
q=1
the sequence will be 2,2,2,2
PS:q^2 means to square 2.