(a)[3]
In a geometric progression, the 3rd and 4th terms are $48$ and $32$ respectively. Find the sum to infinity of the progression.
(b)[5]
Two schemes are suggested for increasing the amount of household waste that is recycled each week. Scheme $A$ is to increase the amount of waste recycled each month by $0.16$ tonnes. Scheme $B$ is to increase the amount of waste recycled each month by $6\%$ of the amount recycled in the previous month. The proposal is to run the scheme for a period of $24$ months. The amount recycled in the first month is $2.5$ tonnes. For each scheme, find the total amount of waste that would be recycled over the $24$-month period.