# 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 4^{th} term with expression of 2^{nd} 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 2^{nd} and 4^{th} 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;

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