### Sequences

Review question

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 $£$.
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?