It is given that
a, b, c, d are in continued proportion
Here we get
a/b = b/c = c/d = k
\[c\text{ }=\text{ }dk,\text{ }b\text{ }=\text{ }ck\text{ }=\text{ }dk\text{ }.\text{ }k\text{ }=\text{ }d{{k}^{2}}\]
\[a\text{ }=\text{ }bk\text{ }=\text{ }d{{k}^{2}}~.\text{ }k\text{ }=\text{ }d{{k}^{3}}\]
Therefore, LHS = RHS.