# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | Oct-Nov | (P1-9709/13) | Q#5

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**Question**

The first term of a geometric progression is and the fourth term is . Find

** i. **the common ratio,

** ii. **the sum to infinity.

**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:

Expressions for 4^{th} term can be written as;

ii.

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

For the given case;

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