If a, b, c are GP, then show that , are in AP.

Question

Philoid · Accepted Answer

To prove: , are in AP.

Given: a, b, c are in GP

Formula used: (i)

As, a, b, c are in GP

⇒

Taking log both side

⇒ log b – log a = log c – log b

⇒ 2log b = log a + log c

Dividing by log m

⇒

Whenever any number a,b,c are in AP then 2b = a+c, considering this and the above equation we can say that , are in AP

Hence proved