Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2008 | January | Q#7
A sequence is given by:
where p is a constant (p≠0)
a. Find x2 in terms of p.
b. Show that x3=1+3p+2p2.
Given that x3=1,
c. find the value of p,
d. (d) write down the value of x2008 .
We are given the sequence as;
We are required to find x2.
We are required to find x3.
x3=(p)(2p)+(p)(1)+ (1)(2p)+ (1)(1)
We have found in (b) that;
We are given that x3=1.
We are required to find p.
Substitute x3=1 in above equation.
Now we have two options.
We are given that p≠0, therefore, .
We are given that sequence is;
We have also found in (c) that;
It is evident that all odd terms are the same and similar is the case of even terms.
We are required to find x2008 which is an even term, therefore;