F.5 Maths geometric sequence

A dog walks along a straight road AB. In the first minute, it walks 54m from point A towards B. In the second minute, it walks 36m towards A. In each succeeding
minute it walks 2/3 of the distance that it walked in the previous minute with
opposite direction. After 9 minutes, it stops at a point Q. Find the distance between the points A and Q.

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