An environmental initiative requires a company to make monthly carbon-offset payments. The payment in the first month is P1=£4,250P_1 = £4,250P1=£4,250, and the payment in the second month is P2=£5,375P_2 = £5,375P2=£5,375. The monthly payments PnP_nPn follow an arithmetic progression. The final payment made is £54,875£54,875£54,875.
Find
the total number of months for which the company made payments,
the total sum of all carbon-offset payments made over the duration of the initiative.
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.