The third term of a geometric progression is 32 and the fifth is 128. Find the first term and the common ratio.
\[
a_n = a_1r^{n-1}
\]
\[
a_3 = a_1r^{n-1}
\]
\[
32 = a_1r^{n-1}
\]
\[
a_5 = a_1r^{n-1}
\]
\[
128 = a_1r^{n-1}
\]
\[
\therefore a_1 = 12.70 \leftarrow \text{answer}
\]
\[
r = 1.59 \leftarrow \text{answer}
\]