Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2009  OctNov  (P19709/12)  Q#3
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Question
A progression has a second term of 96 and a fourth term of 54. Find the first term of the progression in each of the following cases:
i. the progression is arithmetic,
ii. the progression is geometric with a positive common ratio.
Solution
i.
From the given information, we can compile following data for Arithmetic Progression (A.P);
Expression for the general term
We can express both 2^{nd} and 4^{th} terms in this way;




Now that we have these two equations relating
To find
ii.
From the given information, we can compile following data for Geometric Progression (G.P);
Expression for the general term
We can express both 2^{nd} and 4^{th} terms in this way;




Now that we have these two equations relating
Since common ratio is positive;
From the general expression of 2^{nd} term;
Substituting;
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