An arithmetic series is given by
∑n=1150(bn+c)\sum_{n=11}^{50} (bn + c)∑n=1150(bn+c)
where b b\,b and c c\,c are constants. The sum of the series is 2680.
Show that 61b+2c=13461b + 2c = 13461b+2c=134.
Given that the 21st term of the sequence un=bn+cu_n = bn + cun=bn+c is 4 times its 3rd term, find the value of b b\,b and the value of ccc.
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.