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.
Practise AQA A Level Maths 1.7 D: Sequences and series with exam-style questions for A Level Maths. 267 questions covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 Sequences and series in modelling (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
