An arithmetic series is defined by the expression
∑r=837(4r−3) \sum_{r=8}^{37} (4r - 3) r=8∑37(4r−3)(i) Write down the first term of the series. (ii) Write down the common difference of the series. (iii) Find the number of terms of the series.
The energy output of a turbine across various operating frequencies is modeled by a different arithmetic series
∑r=2079(kr+m) \sum_{r=20}^{79} (kr + m) r=20∑79(kr+m)where kkk and mmm are constants. The total energy output of this series is 10980 units. (i) Show that 49.5k+m=18349.5k + m = 18349.5k+m=183. (ii) The 21st term of the series is 15 more than twice the 1st term. Find the values of kkk and mmm.
178 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.