An arithmetic series is defined by its first term a a\,a and common difference ddd. Prove that the sum of the first n n\,n terms is given by the formula:
Sn=n2[2a+(n−1)d] S_n = \frac{n}{2}[2a + (n-1)d] Sn=2n[2a+(n−1)d]A model for the hourly energy output, EkE_kEk (in Joules), of a pulsing laboratory generator during the kkk-th hour is given by:
Ek=7k+3(−1)k E_k = 7k + 3(-1)^k Ek=7k+3(−1)kDetermine the value of: E12E_{12}E12
∑k=161Ek\sum_{k=1}^{61} E_k∑k=161Ek
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.
