3.11 Geometric Sequences

For each sequence, determine if the sequence is a geometric sequence. If so, identify the common ratio.

1. $\left\{5 , 20 , 80 , 320 , 1,280 , 5,120 , 20,480 , ...\right\}$
2. $\left\{- 3 , 6 , - 12 , 24 , 11 , 33\right\}$
3. $\left\{4 , 2 , 1 , \frac{1}{2} , \frac{1}{4} , \frac{1}{8} , ...\right\}$

In the following geometric sequences, determine the indicated term of the geometric sequence with a given first term and common ratio.

1. Determine the $9 \text{th}$ term of the geometric sequence with $a_{1} \times 6$ and $r = 3$.
2. Determine the $11 \text{th}$ term of the geometric sequence with $a_{1} = 2$ and $r = - 5$.

1. What is the sum of the first 13 terms of the geometric sequence with first term $a_{1} = 5$ and common ratio $r = 3$?
2. What is the sum of the first 7 terms of the geometric sequence with first term $a_{1} = 16$ and common ratio $r = \frac{1}{8}$?

Daryl deposits $1,000 in an account earning $4 \%$ interest compounded yearly. How much money is in the account after 25 years?

When Escherichia coli (E. coli) is in a broth culture at 37°C, the population of E. coli doubles in number with 30 organisms, how many E. coli bacteria are present in the culture after 16 hours?

A player places one grain of rice on the first square of a chess board. On the second square, the player places 2 grains of rice. On the third square, the player places 4 grains of rice. On each successive square of the board, the player doubles the number of grains of rice placed on the chess board. When the player places the last rice on the 64th square, how many total grains of rice have been p…