The total energy E(n)E(n)E(n) released by a sequence of n n\,n laser pulses in a laboratory experiment is given by the sum E(n)=∑j=0n(2j)4E(n) = \sum_{j=0}^{n} (2j)^4E(n)=∑j=0n(2j)4 millijoules, where n n\,n is a positive integer. The specific energy produced by the nnn-th pulse is defined as P(n)=E(n)−E(n−1)P(n) = E(n) - E(n-1)P(n)=E(n)−E(n−1).
Determine the specific energy released by the 3rd pulse, P(3)P(3)P(3), and the 10th pulse, P(10)P(10)P(10).
Find the pulse number n n\,n such that the specific energy released is P(n)=8.1×109P(n) = 8.1 \times 10^9P(n)=8.1×109 millijoules.
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.
