An arithmetic series has first term a a\,a and common difference ddd. The sum of the first n n\,n terms of the series is SnS_nSn.
By writing Sn S_n\,Sn out both forwards and in reverse, and adding the two expressions, prove that
Sn=12n[2a+(n−1)d]S_n = \tfrac{1}{2}n\left[2a + (n - 1)d\right]Sn=21n[2a+(n−1)d]
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.