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1.4.9 Geometric sequences and series (A-level only)

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Question 24

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+10

where kkk is a constant.

a.

Prove that k2+5k−150=0k^2 + 5k - 150 = 0k2+5k−150=0.

[3]
b.

Determine the volume of data predicted to be captured in year 4.

[2]
c.

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.

[4]

1.4.9 Geometric sequences and series (A-level only) Questions

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