Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2015  MayJun  (P19709/13)  Q#9
Question
a) The first term of an arithmetic progression is −2222 and the common difference is 17. Find the value of the first positive term.
b) The first term of a geometric progression is and the second term is , where . Find the set of values of for which the progression is convergent.
Solution
a)
From the given information, we can compile following data about Arithmetic Progression (A.P);
Expression for the general term in the Arithmetic Progression (A.P) is:
Since we are looking for the first positive term i.e.
Hence the first positive term is;
b)
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;
A geometric series is said to be convergent if (or ).
Hence;
We have two options;












Hence;
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