■ No GDC ■for SL and HL studentsThe first three terms of a geometric sequence are \(\dfrac{{x\left( {x + 1} \right)}}{{x - 2}}\), \(\dfrac{{x{{\left( {x + 1} \right)}^2}}}{{{{\left( {x - 2} \right)}^2}}}\) and \(\dfrac{{x{{\left( {x + 1} \right)}^3}}}{{{{\left( {x - 2} \right)}^3}}}\), where \(x < 2\).(a) Write down a simplified expression for the common ratio of the sequence.(b) Find a simplified expression for the \(n\)th term of the sequence.(c) Show that the sum of the first \(n\) terms of the sequence, \({S_n}\), is \(\dfrac{x}{3}\left( {x + 1} \right)\left[ {\dfrac{{{{\left( {x + 1} \right)}^n}}}{{{{\left( {x - 2} \right)}^n}}} - 1} \right]\).