First in order to find the pattern, you need to find the number of pounds that the puppy gained from birth to a week after birth.
5 1/8 - 3 3/4=5 1/8 - 3 6/8=4 9/8 - 3 6/8=1 3/8 pounds gained
(1 3/8)(3)=(11/8)(3/1)=33/8=4 1/8 pounds gained
4 1/8 + 3 3/4=4 1/8 + 3 6/8=7 7/8 pounds at week 3