We are given the positive numbers a,b,c, which form an arithmetic progresion in the given order. We know that a+b+c=9. The numbers a+1,b+1,c+3 form a geometric progression in the given order. Find c.  Choose the correct choice from the following:
A) 5  B) 6  C) 7  D) 8  E) 9
Solution:   Since a,b,c form an arithmetic progression, c=b+d=a+2d and a+b+c=a+a+d+a+2d=3a+3d=9, so a+d=b=3 and a+c=6=&gt;c=6−a. Since a+1,b+1,c+3 form a geometric progression, we have (b+1)2=(a+1)(c+3), or 16=(a+1)(6−a+3)=(a+1)(9−a)   16=9a+9−a2−a   a2−8a+7=0, therefore a=7 or a=1. But if a=7, c=6−a=6−7=−1&lt;0 and by definition c is positive, so a=7 is not a solution. Therefore a=1 and c=6−a=6−1=5.   5nswer 5
<result>A</result>
We are given the positive numbers a,b,c, which form an arithmetic progresion in the given order. We know that a+b+c=9. The numbers a+1,b+1,c+3 form a geometric progression in the given order. Find c.