If a, b, c are in G.P., prove that the following are also in G.P. : a

1.	If a, b, c are in G.P., prove that the following are also in G.P. : a2, b2, c2
Answer» As a, b, c are in G.P. Therefore b² = ac … (1) We have to prove a², b², c² are in GP or we need to prove: (b²)² = (ac)² {using idea of GM} On squaring equation 1 we get, ⇒ b⁴ = a²c² ⇒ (b²)² = (ac)² Hence a²,b²,c² are in GP

If a, b, c are in G.P., prove that the following are also in G.P. : a2, b2, c2

Answer»

As a, b, c are in G.P.

Therefore b² = ac … (1)

We have to prove a², b², c² are in GP or

we need to prove: (b²)² = (ac)² {using idea of GM}

On squaring equation 1 we get,

⇒ b⁴ = a²c² ⇒ (b²)² = (ac)²

Hence a²,b²,c² are in GP

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If a, b, c are in G.P., prove that the following are also in G.P. : a2, b2, c2

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