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=03r^2 - 2r - 2 = 03r2−2r−2=0
Given 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∞.
Practise Edexcel A Level Maths Sequences and Series with exam-style questions for A Level Maths. 100 questions 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, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.