Initial amount ( a = 2000 ) gallons, weekly loss ( d = -5 ).

After ( n ) weeks the amount left is ( a_n = 2000 - 5n ).

(i) After 20 weeks: [ a_{20} = 2000 - 5\times 20 = 1900. ]

(ii) Half-full means 1000 gallons: [ 2000 - 5n = 1000 \implies 5n = 1000 \implies n = 200. ]

(iii) Empty: [ 2000 - 5n = 0 \implies n = 400. ]

Answers:
(i) 1900 gallons
(ii) 200 weeks
(iii) 400 weeks