Past Papers’ Solutions  Edexcel  AS & A level  Mathematics  Core Mathematics 1 (C16663/01R)  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;
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