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
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.