# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2002 | Oct-Nov | P1-9709/01 | Q#2

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Question

A geometric progression, for which the common ratio is positive, has a second term of 18 and a  fourth term of 8. Find

i.         the first term and the common ratio of the progression

ii.        the sum to infinity of the progression.

Solution

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

i.

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

From the given data, we can write two expressions for two different terms of Geometric Progression (G.P):

By substitution, both expressions reduce to:

Dividing equation of 4th term with expression of 2nd term:

Since  is +ve i.e,  the only possible value of  is:

Now to find , we can substitute value of  in any of the two expressions for 2nd and 4th terms. It is  convenient to use expression.

ii.

Expression for the sum to infinity of the Geometric Progression (G.P) when  or ;

For the given case;