# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | May-Jun | (P1-9709/13) | Q#9

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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; 