# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2007 | June | Q#8

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Question

A sequence  is defined by

, ,

Where  is a positive integer.

a)   Write down an expression for  a in terms of k.

b)  Show that .

c)

i.       Find  in terms of k.

ii.       Show that  is divisible by 10.

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;

We can substitute  from (a);

c)

We are required to find .

It is evident that we need to find sum of first 4 terms of given arithmetic sequence.

We are already given first term and have found 2nd and 3rd terms in (a) and (b).

We need to find 4th term.

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

We can substitute  from (a);

Therefore;

d)

We are required to show that  is divisible by 10.

We have found in (c) that;

It is evident that since  has a factor 10, therefore, it is divisible by 10.