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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