Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2015  MayJun  (P19709/12)  Q#8
Question
a) The first, second and last terms in an arithmetic progression are 56, 53 and −22 respectively. Find the sum of all the terms in the progression.
b) The first, second and third terms of a geometric progression are 2k + 6, 2k and k + 2 respectively, where k is a positive constant.
i. Find the value of k.
ii. Find the sum to infinity of the progression.
Solution
a)
From the given information, we can compile following data about Arithmetic Progression (A.P);
Expression for difference in Arithmetic Progression (A.P) is:
For the given case;
Expression for the general term in the Arithmetic Progression (A.P) is:
For the given case;
Expression for the sum of number of terms in the Arithmetic Progression (A.P) is:
For the given case;
b)
i.
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 we can have two options;








We can equate the above two expressions of ;
Now we have two options;




According to the given condition is positive.
ii.
Substituting the value of ;
Also in;
Expression for the sum to infinity of the Geometric Progression (G.P) when or ;
For the given case;
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