An arithmetic sequence has first term a a\,a and common difference ddd. The sum of the first 8 terms of the sequence is 198.
Show that 4a+14d=994a + 14d = 994a+14d=99.
Given that the sum of the first 25 terms is 300, find the sum of the first 21 terms.
Sn S_n\,Sn is the sum of the first n n\,n terms of the sequence. Explain why the value you found in part (b) is the maximum value of SnS_nSn.
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.