Question

if a b c are in GP so that a cube b cube C cube also in GP ​

Answer 1

Question:

If a, b, c are in GP, then show that a³, b³, c³ are also in GP .

Answer:

Consider the GP  a, b, c,...

As it's GP, each consecutive term are multiplied up by a constant, which means there's common ratio.

∴  b/a = c/b

Cubing both sides,

(b/a)³ = (c/b)³     →     (1)

Consider the progression  a³, b³, c³,...

As this progression has to be a GP, there should also be common ratio.

Thus,  b³/a³ = c³/b³

⇒ (b/a)³ = (c/b)³

We reached the equation (1).

Hence Proved!!!

Answer 2

Answer:

Step-by-step explanation:

GIVEN   a,b, c  are in GP

             b=ar   and c =ar^2

b^3 =a^3r^3    and c^3 =a^3r^6     take R = r^3

b^3 =a^3 R   and c^3 =a^3 R^2

          a^3,b^3,c^3    are in GP