[MOVED] sequences and series: A finite geomeric sequence has

[kathy's]

A finite geomeric sequence has t₁ = 0.1024 and t₂ = 0.256. How many terms does sequence have, if its middle term has the value 156.25?

How do I do this question? I am confused! Thank you for your help!

 

[pka]

Here is a start anyway:

\(\displaystyle \L
\begin{array}{l}
t_1 = 0.1024,\quad t_2 = 0.256\quad \Rightarrow \quad r = \frac{{t_2 }}{{t_1 }} = 2.5 \\
t_1 r^{n - 1} = 156.25\quad \Rightarrow \quad n = ? \\
2n - 1 = ? \\
\end{array}\)