If `a, b, c` are in `A.P and a, b, d` are in `G.P,` prove that `a, a -b, d -c` are in `G.P.`

Explanation

Given, `a, b, c` are in A.P


Arithmetic mean relation:


`2b=a+c`


`4b^2=a^2+c^2+2ac`


`b-c=a-b`


Given, `a, b, d` are in G.P


Geometric mean relation:


`b^2=ad`



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