Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2016  OctNov  (P19709/11)  Q#5
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Question
The sum of the 1st and 2nd terms of a geometric progression is 50 and the sum of the 2nd and 3^{rd }terms is 30. Find the sum to infinity.
Solution
From the given information, we can compile following data about Geometric Progression (G.P);
Expression for the sum to infinity of the Geometric Progression (G.P) when or ;
Therefore, we need and to find sum to infinity of Geometric Progression (G.P).
Expression for the general term in the Geometric Progression (G.P) is:
Therefore;
Substituting expressions of both and in above equation;










Comparing the two equations;
We can also find by substituting in any one of the above two equations. We choose;
Finally, we can find the sum to infinity of Geometric Progression (G.P).
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