Given series : log3 2 , log6 2 , log12 2
Reciprocals of respective term in given series : log2 3 , log2 6 , log2 12
Sum of first and third term of above series = log2 3 + log2 12 = log2 36 = 2 log2 6
Hence middle term is average of first and third term and the series is in A.P.
Since reciprocals of respective terms of given series are in A.P, Given series is in H.P