Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2015  OctNov  (P19709/11)  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 3^{rd} 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 3^{rd} term in Geometric Progression (G.P);
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