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−rS_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 3.4 Geometric Series with exam-style questions for A Level Maths. 27 questions, 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.