Question

What is k so that k-3,k+2,k+3 form a geometric sequence.

Answer 1

Given:

The sequence is,

`k-3,k+2,k+3`

Suppose that the given sequence is in the geometric sequence. The common ratio will be the same.

`\begin{gathered} (k+2)/(k-3)=(k+3)/(k+2) \\ (k+2)(k+2)=(k+3)(k-3) \\ k^2+4k+4=k^2-9 \\ 4k=-9-4 \\ 4k=-13 \\ k=-(13)/(4) \end{gathered}`

Answer: option c) -13/4