The volume of telemetry data, DDD, in petabytes, captured by a deep-space relay station is observed over its first three years of operation. The data volumes for years 1, 2, and 3 are modeled as the first three terms of a geometric series and are given by
2k−15,k,k+10 2k - 15, \quad k, \quad k + 10 2k−15,k,k+10where kkk is a constant.
Prove that k2+5k−150=0k^2 + 5k - 150 = 0k2+5k−150=0.
Determine the volume of data predicted to be captured in year 4.
The cumulative volume of data captured since the start of operation is predicted to exceed 5×1065 \times 10^65×106 petabytes for the first time in year NNN. Calculate the value of NNN.
326 exam-style questions on Edexcel A Level Maths Sequences and Series, 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. Each one has a worked solution and a mark scheme showing where the marks go.