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
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.