Question

a,b and c are in AP and b-a,c-b and a are In gp then a:b:c is

Answer 1

hope it helps.......

Answer 2

Answer:

1 : 2 : 3

Step-by-step explanation:

Since ,  a, b ,c are in AP;

So,  equating the common difference of the given AP;

b-a = c-b

b = (a+c)/2...........(1)

Now, since;

b-a , c-b and a are in gp;

So ,equating the common ratio of the GP, we get;

So, c-b = $\sqrt{(b-a) \times a}$......(2)

putting the value of b in equation (2);

c - (a+c)/2 = $\sqrt{a \times [\frac{a+c}{2}-a] }$

(c-a)/2 = $\sqrt{a \times \frac{(c-a)}{2} }$

(c-a)/2 = a

c = 3a

put c in eq (1)

we get ;

b = 2a

So, the ratios between a , b and c are  a : 2a : 3a

= 1 : 2 :3

So , the ratios are 1 : 2 : 3