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3.4.5 Sequences and Series (A-level only)

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Question 21

A chemical reaction is monitored at regular time intervals, and the concentration of the remaining catalyst, CCC, is found to follow a geometric progression with first term aaa and common ratio rrr, where r>0r > 0r>0.

Given that:

  • the concentration at the 2nd interval is 54 mg/L
  • the concentration at the 4th interval is 24 mg/L
a.

Show that r=23r = \frac{2}{3}r=32​.

[2]
b.

Determine the value of aaa.

[1]
c.

Given that the sum of the concentrations recorded over the first nnn intervals is greater than 242.5 mg/L

Find the smallest possible value of nnn.

(Solutions based entirely on graphical or numerical methods are not acceptable.)

[4]

3.4.5 Sequences and Series (A-level only) Questions

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