Algebra 2 Practice Test: Sequences, Series and Statistics
- Sequences, Series and Statistics
- 15 questions
- 20 minutes
These 15 questions practice arithmetic and geometric sequences, explicit and recursive formulas, finite and infinite series, sigma notation, the normal distribution, z-scores, sampling methods and margin of error. In both kinds of sequences the nth term uses n − 1 steps from the first term.
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Question 1
What is the 20th term of the arithmetic sequence 7, 11, 15, 19, …?
Correct answer: B
an = a1 + (n − 1)d = 7 + 19 · 4 = 83. Using 20 steps instead of 19 gives 87.
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Question 2
What is the 8th term of the geometric sequence 3, −6, 12, −24, …?
Correct answer: D
an = 3(−2)n − 1, so a8 = 3(−2)7 = 3(−128) = −384. Even-numbered terms of this sequence are negative, which rules out 384.
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Question 3
What is the sum of the first 25 terms of the arithmetic series 5 + 9 + 13 + …?
Correct answer: A
The 25th term is 5 + 24 · 4 = 101, and S25 = 25(5 + 101)2 = 1325. Forgetting to divide by 2 gives 2,650.
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Question 4
What is the sum of the first 6 terms of the geometric series 2 + 6 + 18 + …?
Correct answer: C
Sn = a1(rn − 1)r − 1 = 2(36 − 1)2 = 728. The value 486 is only the 6th term, 2 · 35.
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Question 5
What is the sum of the infinite geometric series 24 + 12 + 6 + 3 + …?
Correct answer: D
The ratio is r = 12, and |r| < 1, so S = a11 − r = 2412 = 48.
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Question 6
What is the value of ∑k=15 (2k + 1)?
Correct answer: B
Add the terms for k = 1 to 5: 3 + 5 + 7 + 9 + 11 = 35. Starting at k = 0 and stopping at 4 gives 1 + 3 + 5 + 7 + 9 = 25.
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Question 7
A sequence is defined by a1 = 4 and an = 2an − 1 − 3 for n ≥ 2. What is a4?
Correct answer: C
a2 = 2(4) − 3 = 5, a3 = 2(5) − 3 = 7, a4 = 2(7) − 3 = 11. The value 7 is a3, one step short.
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Question 8
Which explicit formula describes the geometric sequence 5, 15, 45, 135, …?
Correct answer: A
The first term is 5 and each term is 3 times the previous one, so an = 5 · 3n − 1. With 3n the first term would be 15.
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Question 9
Test scores are normally distributed with a mean of 70 and a standard deviation of 8. About what percent of scores fall between 62 and 86?
Correct answer: B
62 is 1 standard deviation below the mean and 86 is 2 above. By the empirical rule that is 34% + 34% + 13.5% = 81.5%. 68% would cover only 62 to 78.
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Question 10
On a test with mean 72 and standard deviation 5, Jordan scored 85. What is his z-score?
Correct answer: A
z = 85 − 725 = 135 = 2.6. The value 13 is the difference from the mean before dividing by the standard deviation.
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Question 11
A principal wants to estimate how many hours per week students at her school spend on homework. Which method is most likely to produce an unbiased sample?
Correct answer: D
A random sample from the whole roster gives every student the same chance of being chosen. Students in the library or volunteers who answer online are likely to differ from the typical student in how much homework they do.
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Question 12
Which study is an experiment rather than an observational study?
Correct answer: B
In an experiment the researcher assigns the treatment, here by random assignment to the apps. In the other studies people choose their own behavior, and the researcher only observes it.
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Question 13
A poll finds that 62% of a sample of voters support a new park, with a margin of error of 4 percentage points. Which interval is a plausible range for the percent of all voters who support it?
Correct answer: C
The margin of error is added to and subtracted from the sample result: 62 ± 4 gives 58% to 66%. Halving the margin gives 60% to 64%.
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Question 14
Which data set has the greatest standard deviation?
Correct answer: D
Standard deviation measures how far values spread from the mean. {2, 8, 14, 20} has gaps of 6 between values, so it is the most spread out (about 6.7). {5, 5, 5, 5} has standard deviation 0.
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Question 15
A theater has 20 rows. The first row has 18 seats, and each row has 2 more seats than the row in front of it. How many seats are in the theater?
Correct answer: C
The last row has 18 + 19 · 2 = 56 seats, so the total is 20(18 + 56)2 = 740. 56 is only the number of seats in the last row.
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