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

Hits: 16

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.