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∞.
326 exam-style questions on Edexcel A Level Maths Sequences and Series, covering 3.1 Arithmetic Sequences, 3.2 Arithmetic Series, 3.3 Geometric Sequences, 3.4 Geometric Series, 3.5 Sum to Infinity, 3.6 Sigma Notation, 3.7 Recurrence Relations, and 3.8 Modelling with Series. Each one has a worked solution and a mark scheme showing where the marks go.