MATHEMATICS · Multi-part · CBSE · Mathematics · Sequences and Series · Sequences and Series
Problem
Let three real numbers be k−3,k,k+6.
(i) Find all real values of k for which these numbers are consecutive terms of an arithmetic progression.
(ii) Find all real values of k for which these numbers are consecutive terms of a geometric progression arranged in the given order.
(iii) From your answers to parts (i) and (ii), determine whether there exists a value of k for which the three numbers can be both an arithmetic progression and a geometric progression. Give reasons for your conclusion.