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Let us take a=xr b=xr^2 c=xr^3

Now if we take log,

log(xr)                                 log (xr^2)                  log(xr^3)
log (x) +log (r)              log (x)+2log(r)                log (x)+3log(r)

From this we can clearly say that it is in AP with common difference of log(r)

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