Past Papers’ Solutions  Edexcel  AS & A level  Mathematics  Core Mathematics 1 (C16663/01)  Year 2009  January  Q#9
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Question
The first term of an arithmetic series is a and the common difference is d.
The 18^{th} term of the series is 25 and the 21^{st }term of the series is .
a. Use this information to write down two equations for a and d.
b. Show that a = –17.5 and find the value of d.
The sum of the first n terms of the series is 2750.
c. Show that n is given by
d. Hence find the value of n.
Solution
a.
We are given that point following data of Arithmetic Series;
Expression for the general term in the Arithmetic Progression (A.P) is:
Therefore, for both 18^{th} and 21^{st} terms we can write equations as;
For 18^{th} term; 
For 21^{st} term; 




b.
We have found two equations in terms of a and d in (a).
We can simultaneously solve these two equations.
We can write both equations for ‘a’ as follows;
Equating both equations;
Substituting in any of the above two equations yields ‘a’;
c.
We are given that sum of first ‘n’ terms of arithmetic series is 2750.
Expression for the sum of number of terms in the Arithmetic Progression (A.P) is:
Therefore;
Substituting values of ‘a’ and ‘d’ from (a) we get;
d.
We are required to find the value of ‘n’.
From (c) we have;
Now we have two options.






Since ‘n’ represents total number of terms being added, therefore, it cannot be negative. Hence;
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