conservation of linear momentum

Neutrons in a nuclear reactor have the Kinetic energy J . The kinetic energy of the neutron is reduced to by a series of collision between the neutron and carbon nuclei in the moderator . On average , the fractional loss of the kinetic energy of the neutron after each collision is 0.14 . how many collisions does a neutron experience in the process ?

My working :

Let the initial Kinetic energy :

Kinetic energy after 1 collision =

After n collisions , the kinetic energy will be

(1) or

(2)

Which one is the correct one and why is it so ?? Thanks for your time .