The volume of water VnV_nVn (in megalitres) in a reservoir at the end of year n n\,n is modeled by the recurrence relation Vn+1=kVn+50V_{n+1} = kV_n + 50Vn+1=kVn+50, where k k\,k is a constant and V1=200V_1 = 200V1=200.
Find an expression, in terms of kkk, for the volume V2V_2V2.
It is given that the volume at the end of the third year is V3=152V_3 = 152V3=152 megalitres.
Show that k k\,k satisfies the equation 100k2+25k−51=0100k^2 + 25k - 51 = 0100k2+25k−51=0.
Given that the volume of the reservoir is strictly decreasing year-on-year, find the value of V4 V_4\,V4 and the value of V5V_5V5.
The volume of water in the reservoir approaches a limit L L\,L as n→∞n \rightarrow \inftyn→∞.
Write down an equation for LLL.
Find the value of LLL.
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.
