A series of robotic pulses is programmed such that the energy, EkE_kEk, of the kkk-th pulse follows a geometric sequence with first term aaa Joules and common ratio rrr, where r>0r > 0r>0.
Given that
Show that r=23r = \frac{2}{3}r=32.
Determine the value of aaa.
Given that the total energy released by the first nnn pulses is greater than 480480480 Joules,
find the smallest possible value of nnn.
(Solutions based entirely on graphical or numerical methods are not acceptable.)
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.