In an arithmetic sequence, the rrr-th term is given by ur=u1+(r−1)du_r = u_1 + (r-1)dur=u1+(r−1)d, where u1 u_1\,u1 is the first term and d d\,d is the common difference.
Show that the sum of the first n n\,n terms of the corresponding arithmetic series is
Sn=n2(2u1+(n−1)d) S_n = \frac{n}{2}(2u_1 + (n-1)d) Sn=2n(2u1+(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.