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.)
Practise Edexcel A Level Maths Sequences and Series with exam-style questions for A Level Maths. 156 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.
