Algebra Homework – December 3/4
Write an equation for each problem, then clearly show your solution pathway. Your
goal is WAY MORE than “getting the right answer”! It’s all about the process!!
1.
Given 𝑎32 = −337 and 𝑎40 = −425 are two terms in an arithmetic sequence,
find the explicit form of the sequence.
2.
Given 𝑎45 = −808 and 𝑎20 = −383 are two terms in an arithmetic sequence,
find the explicit form of the sequence.
3.
Given 𝑎13 = −94 and 𝑎41 = −346 are two terms in an arithmetic sequence,
find the explicit form of the sequence.
4.
Given 𝑎35 = 436 and 𝑎12 = 68 are two terms in an arithmetic sequence,
find the explicit form of the sequence.
5.
Given a geometric sequence with a 6th term of 1,562.5 and a common ratio
5
of 2, find the explicit form of the sequence.
6.
Given a geometric sequence with a 7th term of 75,776 and a common ratio
of 4, find the explicit form of the sequence.
7.
Given a geometric sequence with a 6th term of 91.125 and a 1st term of 12,
find the explicit form of the sequence.
8.
Given a geometric sequence with a 1st term of 46 and an 8th term of 5,888,
find the explicit form of the sequence.
9.
At the end of 2014, the population of Kenturi was 4,651. The population of
Kenturi has been increasing by 2.9% each year. If the population continues to
increase by the same percent each year, what do you anticipate the population
of Kenturi to be in 2020?
10.
At the end of 2014, the population of Henten, Wisconsin was 38,157. The
population of Henten has been increasing by 1.7% each year. If the population
continues to increase by the same percent each year, what do you anticipate the
population of Henten to be in 2032?
11.
At the end of 2014, the population of Houakev was 7,512. The population of
Houakev has been increasing by 3.2% each year. If the population continues to
increase by the same percent each year, what do you anticipate the population of
Houakev to be in 2028?
12.
At the end of 2014, the population of Julzona was 193,180. The population of
Julzona has been increasing by 2.6% each year. What was the approximate
population of Julzona to be in 2010?
Answers:
1.
𝑎𝑛 = 15 − 11𝑛
2.
𝑎𝑛 = −43 − 17𝑛
3.
𝑎𝑛 = 23 − 9𝑛
4.
𝑎𝑛 = −124 + 16𝑛
5.
𝑎𝑛 = 16 (2)
6.
𝑎𝑛 = 18.5(4)𝑛−1
7.
𝑎𝑛 = 12 (2)
8.
𝑎𝑛 = 46(2)𝑛−1
9.
≈ 5,520
10.
≈ 51,683
11.
≈ 11,675
12.
≈ 174,330
5 𝑛−1
3 𝑛−1
Algebra Homework – December 1/2
Write an equation for each problem, then clearly show your solution pathway. Your
goal is WAY MORE than “getting the right answer”! It’s all about the process!!
1.
Given 𝑎32 = −337 and 𝑎40 = −425 are two terms in an arithmetic sequence,
find the explicit form of the sequence.
2.
Given 𝑎45 = −808 and 𝑎20 = −383 are two terms in an arithmetic sequence,
find the explicit form of the sequence.
3.
Given 𝑎13 = −94 and 𝑎41 = −346 are two terms in an arithmetic sequence,
find the explicit form of the sequence.
4.
Given 𝑎35 = 436 and 𝑎12 = 68 are two terms in an arithmetic sequence,
find the explicit form of the sequence.
5.
Given a geometric sequence with a 6th term of 1,562.5 and a common ratio
5
of 2, find the explicit form of the sequence.
6.
Given a geometric sequence with a 7th term of 75,776 and a common ratio
of 4, find the explicit form of the sequence.
7.
Given a geometric sequence with a 6th term of 91.125 and a 1st term of 12,
find the explicit form of the sequence.
8.
Given a geometric sequence with a 1st term of 46 and an 8th term of 5,888,
find the explicit form of the sequence.
9.
At the end of 2014, the population of Kenturi was 4,651. The population of
Kenturi has been increasing by 2.9% each year. If the population continues to
increase by the same percent each year, what do you anticipate the population
of Kenturi to be in 2020?
10.
At the end of 2014, the population of Henten, Wisconsin was 38,157. The
population of Henten has been increasing by 1.7% each year. If the population
continues to increase by the same percent each year, what do you anticipate the
population of Henten to be in 2032?
11.
At the end of 2014, the population of Houakev was 7,512. The population of
Houakev has been increasing by 3.2% each year. If the population continues to
increase by the same percent each year, what do you anticipate the population of
Houakev to be in 2028?
12.
At the end of 2014, the population of Julzona was 193,180. The population of
Julzona has been increasing by 2.6% each year. What was the approximate
population of Julzona to be in 2010?
Answers:
1.
𝑎𝑛 = 15 − 11𝑛
2.
𝑎𝑛 = −43 − 17𝑛
3.
𝑎𝑛 = 23 − 9𝑛
4.
𝑎𝑛 = −124 + 16𝑛
5.
𝑎𝑛 = 16 (2)
6.
𝑎𝑛 = 18.5(4)𝑛−1
7.
𝑎𝑛 = 12 (2)
8.
𝑎𝑛 = 46(2)𝑛−1
9.
≈ 5,520
10.
≈ 51,683
11.
≈ 11,675
12.
≈ 174,330
5 𝑛−1
3 𝑛−1