Algebra 3
Test Review – Module 12
Write an explicit rule and a recursive rule for each sequence.
1.
.
n
1
2
3
4
…
f(n)
15
13
11
9
…
n
1
2
3
4
…
f(n)
!
!"
!
!
1
5
…
2.
3. Complete the table of values for the sequence f(n) = -1 + 2n, n ≥ 1. Then draw the
graph of the sequence.
n
1
2
3
4
f(n)
4. The population of a town is 20,000. It is expected to grow at 4% per year.
a. Write a recursive rule and an explicit rule to predict the population, p(n), n years
from today.
b. Use a rule to predict the population in 5 years and in 10
years.
5. A geometric series begins with 1000 and decreases by 25% successively.
a. Determine the common ratio.
b. In the sum formula, determine the values of a and r.
c. Find the sum, if the series has 5 terms. Round to the nearest integer.
d. Find the sum, if the series has 10 terms. Round to the nearest integer.
6. Given the recursive rule for an arithmetic sequence, write the explicit rule and
complete the table of values.
f(0) = -4 and f(n) = f(n - 1) + 5 for n ≥ 1
n
f(n)
1
2
3
4
5
6
7.
( )
Complete the table of values for the sequence f (n) = 3 2
n−1
, n ≥ 1. Then draw
the graph of the sequence.
n
f(n)
1
2
3
4
5
...
...
8. Determine the number of terms that are included in each geometric series and find the
sum of the series. Round the sum to the nearest whole number if necessary.
162 + 54 + 18 + ... +
Number of terms:
Sum:
2
27