A modular structural analysis of a skyscraper uses a load-bearing index L(m)L(m)L(m) for the mmm-th floor. This index is calculated by the difference between two cumulative load sums:
L(m)=∑k=0m5k4−∑k=0m−15k4 L(m) = \sum_{k=0}^{m} 5k^4 - \sum_{k=0}^{m-1} 5k^4 L(m)=k=0∑m5k4−k=0∑m−15k4where mmm is a positive integer representing the floor number.
Find the load-bearing index for the 4th floor, L(4)L(4)L(4), and the 10th floor, L(10)L(10)L(10).
An engineer determines that the maximum theoretical limit for a floor's load-bearing index is 3.125×10113.125 \times 10^{11}3.125×1011. Calculate the floor number mmm that reaches this limit.
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.
