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Answer:
[tex]-\frac{1}{128}[/tex]
Step-by-step explanation:
1) Identify the type of sequence this is; whether it is geometric progression, quadratic sequence or linear sequence.
= Geometric progression
2) Find the [tex]n^{th}[/tex] term of this sequence. Every sequence of geometric progression is written in [tex]u_{n} = u_{1} * r^{n-1}[/tex] form, where [tex]u_{1}[/tex] is the first term of the sequence and [tex]r[/tex] is the common ratio. To find the [tex]n^{th}[/tex] term of this sequence, we need to find the common ratio ([tex]r[/tex]) first.
[tex]r = \frac{u_{2}}{u_{1}}[/tex]
[tex]r = \frac{-32}{64}[/tex]
[tex]r = -\frac{1}{2}[/tex]
2.1) Write it in [tex]u_{n} = u_{1} * r^{n-1}[/tex] form.
[tex]u_{n} = 64 * (-\frac{1}{2} )^{n-1}[/tex]
3) Find the [tex]14^{th}[/tex] term by substituting 14 into the [tex]n[/tex]'s.
[tex]u_{14} = 64 * (-\frac{1}{2} )^{14-1}[/tex]
[tex]u_{14} = 64 * (-\frac{1}{2} )^{13}[/tex]
[tex]u_{14} = 64 * -\frac{1}{8192}\\u_{14} = -\frac{1}{128}[/tex]