Name that Sequence!
Determine the first 5 terms of the arithmetic sequence defined by an=3+(n-1)(6).
3, 9, 15, 21, 27, ...
Determine the common difference for the following arithmetic sequence:
-9, -5, -1, 3, ...
d=4
Determine the common ratio of the following geometric sequence:
7.4, 6.29, 5.3465, ...
r= 0.85
Find the sum of the series defined from n=1 to n=5 with each term being defined by 2n-1.
S5= 25
Describe a real-world scenario in which you could use arithmetic series to calculate the answer to some question (answers will vary).
Answers will vary (examples: calculating profit after selling items in bulk, etc.)
Determine whether the following sequence is arithmetic or geometric:
2, 4, 8, 16, 32, ...
Geometric
Determine the common difference of the arithmetic sequence defined by an=-12.5+(n-1)(-3)
d= -3
Determine the common ratio of the geometric sequence defined by an=(-2)an-1
r = -2
Find the sum of the series defined from n=1 to n=25 with each term in the sequence defined by 0.5n+4.
S25 = 262.5
Describe a real-world scenario in which you could use geometric sequences to calculate the answer to some question (answers will vary).
Answers will vary (determine value of a house after a certain number of years when it appreciates, car depreciation, etc.).
Describe all of the following about the sequence below: whether its arithmetic or geometric, infinite or finite, and its common ratio or common difference.
-17, -8, 1, 10, 19, ...
Arithmetic, Infinite, d=9
a30 = 278.5
Determine the 19th term of the geometric sequence with a1=7 and r=1.025. Round to the nearest hundredth if necessary.
a19 = 10.92
Find the sum of the series defined from n=1 to n=23 with each term in the sequence defined by 2(2/3)n-1. Round to the nearest hundredth, if necessary.
S89 = 6
If Mr. C decided to buy a house for $300,000 and it appreciates by 2.7% each year, write the first 4 terms of the sequence that represents the value of the house at the end of each year after he buys it.
$308,100, $316,418.7, $324,962.01, $333,735.98, ...
Determine whether the following sequence is arithmetic or geometric AND find its common difference or common ratio.
18, 10.8, 6.48, ...
Geometric, r=.6 or 3/5
-12.15, -9.45, - 6.75, -4.05, ...
Explicit: 2.7n -14.85
Recursive: a1= -12.15, an=an-1 +2.7
Write both the explicit and recursive formulas for the following geometric sequence,
9, -2.34, 0.6084, ...
Explicit: an=9(-0.26)n-1
Recursive: a1=9, an= -.26an-1
Find the sum of the series defined from n=1 to infinity with each term in the sequence defined by -3(4)n-1. Round to the nearest hundredths place, if necessary.
S = Does Not Exist (DNE)
If Mr. C decided to buy a house for $300,000 and it appreciates by 2.7% each year, determine the explicit formula that represents the sequence defined but he context above.
an= 300,000(1.027)n OR an= 308,100(1.027)n-1
Describe all of the following about the sequence below: whether it's arithmetic or geometric, infinite or finite, and its common ratio or common difference.
-13.36, 16.032, -19.2384, 23.08608, ...
Geometric, Infinite, r= -1.2
Determine the first term of the arithmetic sequence with a common difference of 10.25 and a54=345.
a1= -198.25
Determine the common ratio of the geometric sequence with a1= 14 and a57= 1,257. Round to the nearest hundredth if necessary.
r = 1.08
Find the sum of the series defined from n=1 to infinity with each term in the sequence defined by -(1/3)n-1. Round to the nearest hundredths place, if necessary.
S = -1.5
Mr. C decided he wanted to buy a car. He bought the car for $57,000. As soon as he drove it off the lot of the car dealership, it began to depreciate by 3% each year. Write an explicit formula for the sequence defined by the value of the car at the end of each year after Mr. C buys it, and determine the value of the car after 10 years.
an= 57000(.97)n OR an= 55,290(.97)n-1
The value of the car after 10 years would be $42,033.18