In a geometric sequence x1,x2,x3,…x_1, x_2, x_3, \dotsx1,x2,x3,…:
Show that r r\,r satisfies the equation
3r2−2r−2=0 3r^2 - 2r - 2 = 0 3r2−2r−2=0Given that the geometric sequence has a sum to infinity,
find the exact value of x1 x_1\,x1 in the form a+b7a + b\sqrt{7}a+b7 where a,b∈Qa, b \in \mathbb{Q}a,b∈Q.
Hence, calculate the value of S∞S_\inftyS∞.
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.