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 AQA A Level Maths 1.7 D: Sequences and series, covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.