A colour television set is hired for \(£80\) in the first year. In each subsequent year the charge is four-fifth of the charge in the previous year. Write down the first four terms of a geometric progression of payments made in successive years, without working them out individually. Calculate the total paid over 8 years by the hirer to the nearest \(£\).

How can we sum the terms of a geomtric progression? Is there a formula we can use?

If instead he had borrowed \(£200\) to buy the set outright and this debt had accumulated at \(10\%\) compound interest, what total sum to the nearest \(£\) would be owing after 8 years?

Can we write down how much is owed at the end of year 1? At the end of year 2?