Question

evaluate independent practice
learning goal
i can determine an explicit expression or a recursive process.
lesson reflection (circle one)
starting... getting there got it!
complete the previous problems, check your solutions, then complete the lesson checkpoint below.
complete the lesson reflection above by circling your current understanding of the learning goal(s).
write the explicit rule represented by each geometric sequence. select all correct true statements below.
1.

n	1	2	3	4	5
f(n)	8	72	648	5832	52488

the common ratio of the geometric sequence is 8.
the common ratio of the geometric sequence is 9.
the explicit rule for the geometric sequence is 8(9)^(n - 1).
the explicit rule for the geometric sequence is 9(8)^(n - 1).

1. 18, 90, 450, 2250, 11250, ...

the common ratio of the geometric sequence is 5.
the common ratio of the geometric sequence is 10.
the explicit rule for the geometric sequence is 18(5)^(n - 1).
the explicit rule for the geometric sequence is 5(18)^(n - 1).

1. write the explicit rule for the geometric sequence 3, 15, 75, 375, 1875.
2. stefanys salary at her company, horizon logistics, starts at a base salary of $60000. the table below shows her salary g(x) after x years. write an explicit rule for the g(x).

years (x)	salary g(x)
1	60000
2	66000
3	72600
4	79860

Explanation:

Step1: Recall geometric - sequence formula

The explicit formula for a geometric sequence is $f(n)=a_1r^{n - 1}$, where $a_1$ is the first - term and $r$ is the common ratio.

Step2: Solve for sequence 1

Given the sequence with $a_1 = 8$, $f(2)=72$. Calculate the common ratio $r=\frac{f(2)}{f(1)}=\frac{72}{8}=9$. The explicit rule is $f(n)=8\times9^{n - 1}$. So the correct statements are: The common ratio of the geometric sequence is 9; The explicit rule for the geometric sequence is $8(9)^{n - 1}$.

Step3: Solve for sequence 2

For the sequence $18,90,450,2250,11250,\cdots$, $a_1 = 18$, and $r=\frac{90}{18}=5$. The explicit rule is $f(n)=18\times5^{n - 1}$. So the correct statements are: The common ratio of the geometric sequence is 5; The explicit rule for the geometric sequence is $18(5)^{n - 1}$.

Step4: Solve for sequence 3

For the sequence $3,15,75,375,1875,\cdots$, $a_1 = 3$, $r=\frac{15}{3}=5$. The explicit rule is $f(n)=3\times5^{n - 1}$.

Step5: Solve for sequence 4

For the salary sequence, $a_1 = 60000$, $r=\frac{66000}{60000}=1.1$. The explicit rule is $g(x)=60000\times(1.1)^{x - 1}$.

Answer:

1. The common ratio of the geometric sequence is 9; The explicit rule for the geometric sequence is $8(9)^{n - 1}$.
2. The common ratio of the geometric sequence is 5; The explicit rule for the geometric sequence is $18(5)^{n - 1}$.
3. $f(n)=3\times5^{n - 1}$
4. $g(x)=60000\times(1.1)^{x - 1}$