2m-8, 2m+4 and 5m-2 are successive terms of a geometric sequence.  Find the values of m.

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well here, 1st term * 3rd term = 2nd term ^2 (thts how geometric sequence works)thus, (2m-8)(5m-2) = (2m+4)^2  or, 10m^2 - 4m - 40 m + 16  = 4m^2 + 16m + 16or, 6m^2 - 60m = 0or, m^2 - 10m = 0or, m^2 = 10mor m =10Therefore, m = 10which is the required answer.just to make sure, plug in the value back to the question and check2m - 8 = 122m + 4 = 24  ( 12 * 2 )5m - 2 =  48  (24 * 2)thus, its works with common ratio 2. answer is right.