Bertie makes payments into a savings account every month. He pays in £250 in the first month and the amount he pays increases by £50 each subsequent month. Charlotte also makes payments into a savings account. She pays in £400 in the first month and the amount she pays in increases by £20 each subsequent month.
Show that, after n n\,n months, the total amount Bertie has paid in is £25n(n+9)25n(n+9)25n(n+9) and the total amount Charlotte has paid in is £10n(n+39)10n(n+39)10n(n+39).
Hence, after how many months have Bertie and Charlotte paid in the same amount in total.
326 exam-style questions on Edexcel A Level Maths Sequences and Series, covering 3.1 Arithmetic Sequences, 3.2 Arithmetic Series, 3.3 Geometric Sequences, 3.4 Geometric Series, 3.5 Sum to Infinity, 3.6 Sigma Notation, 3.7 Recurrence Relations, and 3.8 Modelling with Series. Each one has a worked solution and a mark scheme showing where the marks go.