Mathematics

Problem

Let three real numbers be

k-3,\; k,\; k+6

. a. (i) Find all real values of

k

for which these numbers are consecutive terms of an arithmetic progression. b. (ii) Find all real values of

k

for which these numbers are consecutive terms of a geometric progression arranged in the given order. c. (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.

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