# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | Oct-Nov | (P1-9709/11) | Q#8

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Question

The first term of a progression is  and the second term is .

i.
For the case where the progression is arithmetic with a common difference of 12, find the  possible values of  and the corresponding values of the third term.

ii.       For the case where the progression is geometric with a sum to infinity of 8, find the third term.

Solution

i.

From the given information, we can compile following data about Arithmetic Progression (A.P);

Expression for difference  in Arithmetic Progression (A.P) is:

For the given case;

Now we have two options.

 For For

Expression for the general term  in the Arithmetic Progression (A.P) is:

To find the 3rd term in Arithmetic Progression (A.P);

 For For

ii.

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

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

For the given case;

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

For the given case;

Hence;

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

To find the 3rd term in Geometric Progression (G.P);