# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/11) | Q#5

Question

The sum of the 1st and 2nd terms of a geometric progression is 50 and the sum of the 2nd and 3rd 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).