The sixth term of an arithmetic series is 12. The sum of the first 16 terms of the series is SnS_nSn and S16=152S_{16} = 152S16=152. Find the first term and common difference of the series.
A second arithmetic series has first term −4-4−4 and common difference 12\frac{1}{2}21. The sum of the first nnn terms of this series is TnT_nTn. Find the value of nnn such that Tn=SnT_n = S_nTn=Sn, where n>0n > 0n>0.
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.