# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2009 | Oct-Nov | (P1-9709/12) | 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  in the Arithmetic Progression (A.P) is:

We can express both 2nd and 4th terms in this way;

Now that we have these two equations relating  and ;

To find  we can use any of the above two equations; we choose equation for 2nd term,

ii.

From the given information, we can compile following data for Geometric Progression (G.P);

Expression for the general term  in the Geometric Progression (G.P) is:

We can express both 2nd and 4th terms in this way;

Now that we have these two equations relating  and ;

Since common ratio is positive;

From the general expression of 2nd term;

Substituting;