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 (MEI) A Level Maths 1.6 Sequences and Series, covering 1.6.1 Binomial expansion for positive integer n, 1.6.2 Factorial and combinations notation, 1.6.3 Binomial expansion for rational n (A-level only), 1.6.4 Binomial expansion of (a + bx)^n via factoring (A-level only), 1.6.5 Binomial approximating polynomials (A-level only), 1.6.6 What a sequence is; finite and infinite (A-level only), 1.6.7 Generate a sequence by formula or recurrence (A-level only), 1.6.8 A series as a sum of terms (A-level only), 1.6.9 Sigma notation (A-level only), 1.6.10 Increasing, decreasing and periodic sequences (A-level only), 1.6.11 Convergent and divergent sequences (A-level only), 1.6.12 Arithmetic sequences and series (A-level only), 1.6.13 Standard formulae for arithmetic series (A-level only), 1.6.14 Geometric sequences and series (A-level only), 1.6.15 Standard formulae for geometric series (A-level only), 1.6.16 Sum to infinity of a geometric series (A-level only), and 1.6.17 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.