2016/092) a,b,c, are 1st 3 terms of a geometric series . if harmonic mean of a,b is 12 and of b,c is 36 find first 5 terms of the series.

let common ratio be t
then terms are a, at
the harmonic mean is 12
so $\frac{1}{a} + \frac{1}{at} = \frac{1}{6}\cdots(1)$
and
$\frac{1}{at} + \frac{1}{at} = \frac{1}{18}$
deiding (1) by (2) we get $t = 3$
now from (1) $\frac{1}{a} + \frac{1}{3a} = \frac{1}{6}$ or a = 8
giving 5 terms 8,24,72,216,648.