You Do Need power plug adapter while traveling from Turkmenistan to Sri Lanka.

Here is Why You Need An Adapter

The outlet and plug type used in Sri Lanka is G and in Turkmenistan are C and F. This is how they look like.

Turkmenistan

In Turkmenistan, outlets of type C and F are in use.

Type C

Type F

Sri Lanka

In Sri Lanka, outlets of type G are in use.

Type G