Find the possible values of the common ratio of a geometric sequence whose first term is $2$ and whose fifth term is $32$ .

For question below, first decide whether the situation is arithmetic or geometric, then solve accordingly.

A frog fell into a $1$ m well and wanted to go back up to the top of the well. Every day it moved up half the distance to the top. After $10$ days, how much did the frog have left to climb?

For question below, first decide whether the situation is arithmetic or geometric, then solve accordingly.

Your grandparents deposit $\$2000$ into a bank account to start a college fund for you. They will continue to deposit a fixed amount each month if you deposit $\$5$ a month as well. In $36$ months, you would like to have $\$6500$ in the account. How much will they have to contribute each month?

For question below, first decide whether the situation is arithmetic or geometric, then solve accordingly.

The Chinese zodiac associates years with animals, based on a $12-$year cycle. Samu was born in $1962$, the Year of the Tiger. He lives in Finland, which celebrated its centennial in $2017$ . Did Finland gain its independence in the Year of the Tiger?

For question below, first decide whether the situation is arithmetic or geometric, then solve accordingly.

A scientist puts six bacteria, which multiply at a constant rate, in a Petri dish. She records the number of bacteria each minute thereafter. If she counts $324$ bacteria $20$ minutes later, at what rate are the bacteria reproducing?