# 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

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;