A damped mechanical oscillator's displacement at the peak of each oscillation forms a geometric sequence. The displacement of the kkk-th peak is given by dk=ark−1d_k = ar^{k-1}dk=ark−1.
Prove that the sum of the displacements for the first n n\,n peaks is given by
Sn=a(1−rn)1−r S_n = \frac{a(1 - r^n)}{1 - r} Sn=1−ra(1−rn)The displacement at the 4th peak is 40 mm and the displacement at the 7th peak is -5 mm.
Determine the value of the common ratio rrr.
Hence calculate the sum of the displacements for the first 10 peaks, giving your answer to 2 decimal places.
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.
