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.
308 exam-style questions on OCR A Level Maths 1.4 Sequences and Series, covering 1.4.1 Binomial expansion for positive integer n, 1.4.2 Link to binomial probabilities, 1.4.3 Binomial expansion for rational n (A-level only), 1.4.4 Validity of the expansion (A-level only), 1.4.5 Sequences (A-level only), 1.4.6 Increasing, decreasing and periodic sequences (A-level only), 1.4.7 Sigma notation (A-level only), 1.4.8 Arithmetic sequences and series (A-level only), 1.4.9 Geometric sequences and series (A-level only), 1.4.10 Sum to infinity of a geometric series (A-level only), and 1.4.11 Modelling with sequences and series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.