# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2010 | May-Jun | (P1-9709/13) | Q#1

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**Question**

The first term of a geometric progression is 12 and the second term is −6. Find

** i. **the tenth term of the progression,

** ii. **the sum to infinity.

**Solution**

i.

** **

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

To find the tenth term;

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

So we need to find the tenth term;

Expression for Common Ratio () in a Geometric Progression (G.P) is;

For the given case;

Now we can find the tenth term;

ii.

Expression for the sum to infinity of the Geometric Progression (G.P) when is:

We can substitute values of and ;

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