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 (MEI) A Level Maths 1.6 Sequences and Series, covering 1.6.1 Binomial expansion for positive integer n, 1.6.2 Factorial and combinations notation, 1.6.3 Binomial expansion for rational n (A-level only), 1.6.4 Binomial expansion of (a + bx)^n via factoring (A-level only), 1.6.5 Binomial approximating polynomials (A-level only), 1.6.6 What a sequence is; finite and infinite (A-level only), 1.6.7 Generate a sequence by formula or recurrence (A-level only), 1.6.8 A series as a sum of terms (A-level only), 1.6.9 Sigma notation (A-level only), 1.6.10 Increasing, decreasing and periodic sequences (A-level only), 1.6.11 Convergent and divergent sequences (A-level only), 1.6.12 Arithmetic sequences and series (A-level only), 1.6.13 Standard formulae for arithmetic series (A-level only), 1.6.14 Geometric sequences and series (A-level only), 1.6.15 Standard formulae for geometric series (A-level only), 1.6.16 Sum to infinity of a geometric series (A-level only), and 1.6.17 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.