Question

Find the geometric means in the following sequence.–14, ? , ? , ? , ? , –235,298 98, 686, 4,802, 33,614–1,960, –2,940, –3,920, –4,900–98, –686, –4,802, –33,614–686, –4,802, –33,614, –235,313

Answer 1

So, notice that:

Given the geometric sequence:

`-14,\ldots,-235298_{}`

There is a common ratio between each term of the sequence:

So we could use the fact that:

`\begin{gathered} -235298=-14\cdot r\cdot r\cdot r\cdot r\cdot r \\ -235298=-14r^5 \end{gathered}`

If we solve this equation for r:

`\begin{gathered} r^5=(-235298)/(-14) \\ \\ r^5=16807 \\ r=\sqrt[5]{16807} \\ r=7 \end{gathered}`

As the common ratio is 7, then, the geometric means are:

`-14,-98,-686,-4802,-33614,-235298`

So the correct answer is C.