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:
Show that r=23r = \frac{2}{3}r=32.
Determine the value of aaa.
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.)
178 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.