SOLUTION: If three numbers a,b,c are in arithmetic progression then: a^2(b+c),b^2(c+a) and c^2(a+b) are in : (a)A.P (b)G.P (c)H.P (d)A.G.P.

Algebra ->  Number-Line -> SOLUTION: If three numbers a,b,c are in arithmetic progression then: a^2(b+c),b^2(c+a) and c^2(a+b) are in : (a)A.P (b)G.P (c)H.P (d)A.G.P.      Log On


   

Question 141139: If three numbers a,b,c are in arithmetic progression then:
a^2(b+c),b^2(c+a) and c^2(a+b) are in :
(a)A.P (b)G.P (c)H.P (d)A.G.P.
Answer by CubeyThePenguin(3113) About Me  (Show Source):
You can put this solution on YOUR website!
This is a repeat question.

a, b, c ---> a-d, a, a+d
a^2(b+c) = (a-d)^2 * (2a + d) = 2a^3 - 3a^2d + d^3
b^2(c+a) = a^2 * (2a) = 2a^3
c^2(b+a) = (a+d)^2 * (2a - d) = 2a^3 + 3a^2d - d^3
This is another arithmetic sequence with common difference 3a^2d - d^3.