so hmmm every two weeks, he'll get 10cents,
week 2 is 10cents
week 4 is 20 cents
week 6 40
and so on.
so, we know for the first week pair he'll be getting 10cents, so let's say the each term in this sequence is a week pair and since there'll 30 weeks, then that means 30/2 or 15 week pairs or 15 terms.
now, the first term is 10, and it doubles from there on, thus the "common ratio" is 2.
[tex]\bf n^{th}\textit{ term of a geometric sequence}\\\\
a_n=a_1\cdot r^{n-1}\qquad
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
a_1=10\\
r=2\\
n=\stackrel{week~pair}{15}
\end{cases}
\\\\\\
a_{15}=10\cdot 2^{15-1}\implies a_{15}=10\cdot 2^{14}
\\\\\\
a_{15}=10\cdot 16384\implies a_{15}=163840~cents[/tex]
now, the 15th term, or 30th week, it'll be 163840 pennies, how many dollars is that? well, 163840/100 or 1638.40.
