# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2013 | June | Q#6

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Question

A sequence is defined by  , Where is a constant, .

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

b)  Show that Given also that c)   Calculate the value of k.

d)  Hence, find the value of .

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;   We are given that ;  b.

We are required to find .

We can utilize the given expression for general terms beyond first term as;   We have found in (a) that ;    c.

We are given that; We have found in (b) that; Therefore;   Now we have two options.      We are given that , therefore; d.

We are given that sequence is defined by  We have found in (c) that; Hence;    Similarly;    Moreover,    We can see that the sequence consists of successive 1 and repetitively.

Therefore, in first 100 terms of the sequence there will be 50 times 1 and 50 times .

Hence, sum of all these 100 terms will be;   