# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | May-Jun | (P1-9709/11) | Q#7

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Question

a)   The third and fourth terms of a geometric progression are and respectively. Find the sum to infinity of the progression.

b)  A circle is divided into 5 sectors in such a way that the angles of the sectors are in arithmetic  progression. Given that the angle of the largest sector is 4 times the angle of the smallest sector,  find the angle of the largest sector.

Solution

a)

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 general term in the Geometric Progression (G.P) is: For the 3rd term we can write;       Expression for the sum to infinity of the Geometric Progression (G.P) when or ; For the given case;     b)

From the given information, we can compile following data about Arithmetic Progression (A.P); Smallest angle will be the first term; Largest angle will be the last (5th) term; Sum of all the angle-sectors in a circle is . Expression for the general term in the Arithmetic Progression (A.P) is: For the 5th term we can write;      Expression for the sum of number of terms in the Arithmetic Progression (A.P) is: For the given case;        This is the smallest angle; we know that largest angle is four times of the smallest angle i.e. 