Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2019  OctNov  (P19709/13)  Q#9
Hits: 35
Question
The first, second and third terms of a geometric progression are , and respectively.
(i) Show that satisfies the equation 7k^{2} − 48k + 36 = 0.
(i) Find, showing all necessary working, the exact values of the common ratio corresponding to each of the possible values of k.
(ii) One of these ratios gives a progression which is convergent. Find the sum to infinity.
Solution
i.
From the given information, we can collect following information about this Geometric Progression (G.P).
Expression for Common Ratio () in a Geometric Progression (G.P) is;
Hence;
ii.
We are required to solve the following equation obtained in (i);
Now we have two options.





Now we can find using these values of and following equation;












iii.
We are required to find the sum to infinity of a progression which is convergent.
A geometric series is said to be convergent if (or ).
Therefore, for the given case;


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