# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | June | Q#5

Question

A sequence of numbers  is defined by

,

Where  is a constant.

a)   Write down an expression, in terms of c, for .

b)  Show that

Given that

c)   Find a range of values of c.

Solution

a)

We are given that sequence  is defined by

We are required to find .

We can utilize the given expression for general terms beyond first term as;

b)

We are required to find .

We can utilize the given expression for general terms beyond first term as;

c)

We are given that;

We know that;

We need to find first .

We can utilize the given expression for general terms beyond first term as;

Therefore;

According to given condition;