Math: Sequences and Series
64x⁶ - 192x⁵y + 240x⁴y² - 160x³y³ + 60x²y⁴ - 12xy⁵ + y⁶
(2x - y)⁶
729r⁶ + 2916r⁵s + 4860r⁴s² + 4320r³s³ + 2160r²s⁴ + 576rs⁵ + 64s⁶
(3r + 2s)⁶
-236 - 115i
(4 - i)⁵
(n + 1)(n + 2)
(n + 2)! / n!
x⁴ + 8x³ + 24x² + 32x + 16
(x + 2)⁴
x⁵ + 10x⁴ + 40x³ + 80x² + 80x + 32
(x + 2)⁵
x² + 2xy + y²
(x + y)²
x³ + 3x²y + 3xy² + y³
(x + y)³
x + y
(x + y)¹
1
(x + y)⁰
x⁴ + 4x³y + 6x²y² + 4xy³ + y⁴
(x + y)⁴
720
6!
0.946
A bag contains 4 red marbles and 6 blue marbles. A marble is drawn and then replaced. This is done 50 times. What is the probability that a red marble is drawn at least 15 times?
0.561
A bag contains 4 red marbles and 6 blue marbles. A marble is drawn and then replaced. This is done 50 times. What is the probability that a red marble is drawn at most 20 times?
0.787
A bag contains 4 red marbles and 6 blue marbles. A marble is drawn and then replaced. This is done 50 times. What is the probability that a red marble is drawn between 17 and 25 times, inclusive?
0.042
A bag contains 4 red marbles and 6 blue marbles. A marble is drawn and then replaced. This is done 50 times. What is the probability that a red marble is drawn exactly 15 times?
3208.53
A bungee jumper is jumping off the New River Gorge Bridge in West Virginia, which has a height of 876 feet. The cord stretches 850 feet and the jumper rebounds 75% of the distance fallen. After jumping and rebounding 10 times, how far has the jumper traveled downward?
5950
A bungee jumper is jumping off the New River Gorge Bridge in West Virginia, which has a height of 876 feet. The cord stretches 850 feet and the jumper rebounds 75% of the distance fallen. Approximate the total distance both downward and upward, that the jumper travels before coming to rest.
2406.4
A bungee jumper is jumping off the New River Gorge Bridge in West Virginia, which has a height of 876 feet. The cord stretches 850 feet and the jumper rebounds 75% of the distance fallen. How far has the jumper traveled upward?
5614.93
A bungee jumper is jumping off the New River Gorge Bridge in West Virginia, which has a height of 876 feet. The cord stretches 850 feet and the jumper rebounds 75% of the distance fallen. What is the total distance traveled downward and upward?
0.175
A pair of dice is rolled 20 times. What is the probability that a sum of 5 is rolled at least 4 times?
0.982
A pair of dice is rolled 20 times. What is the probability that a sum of 5 is rolled at most 5 times?
0.014
A pair of dice is rolled 20 times. What is the probability that a sum of 5 is rolled exactly 6 times?
1343.92
A principal of $1000 is invested at 3% interest. Find the amount after 10 years if the interest is compounded annually.
1349.84
A principal of $1000 is invested at 3% interest. Find the amount after 10 years if the interest is compounded daily.
1349.35
A principal of $1000 is invested at 3% interest. Find the amount after 10 years if the interest is compounded monthly.
1348.35
A principal of $1000 is invested at 3% interest. Find the amount after 10 years if the interest is compounded quarterly.
1346.86
A principal of $1000 is invested at 3% interest. Find the amount after 10 years if the interest is compounded semiannually.
1:40pm CST
A train leaves Chicago at 10am CST on Wednesday. It is heading to Pittsburg. Before arriving in Pittsburg it will stop at 10 locations evenly spaced out two hours apart. At the first stop it will wait 10 minutes and each successive stop it will wait 8 more minutes more than the previous stop. At what time will the train arrive in Pittsburg?
0.518582
Approximately 3% of the eggs in a store are cracked. If you buy two dozen eggs, what is the probability that at least one of your eggs is cracked
0.127
Approximately 3% of the eggs in a store are cracked. If you buy two dozen eggs, what is the probability that exactly two of your eggs are cracked
0.4814172
Approximately 3% of the eggs in a store are cracked. If you buy two dozen eggs, what is the probability that none of your eggs are cracked
Neither
Determine which type of sequence is given (arithmetic, geometric, neither). -6, -2, 1, 3
Neither
Determine which type of sequence is given (arithmetic, geometric, neither). 1, 8, 27, 64
Arithmetic
Determine which type of sequence is given (arithmetic, geometric, neither). 1/3, -1/6, -2/3, -7/6
Geometric
Determine which type of sequence is given (arithmetic, geometric, neither). 2, -10, 50, -250
-236 - 115i
Expand (4 - 5i)³
-5991
Find the 1000th term of the sequence: 3, -3, -9
-316
Find the 13th term of a sequence if the 41st term is 48 and d = 13
2
Find the 1st term of a sequence if the 9th term is 512 and r = -2
940395480
Find the 42nd term of the sequence: 100k, 125k, 156.25k
1120a⁴b⁴
Find the 5th term of (a + 2b)⁸
-11547360
Find the coefficient of the term a⁴b⁷ in the expansion of (2a - 3b)¹¹
0.2, -1.6, -3.4
Find the next 3 terms of the sequence: 5.6, 3.8, 2
-8/3, 16/9, -32/27
Find the next 3 terms of the sequence: 9, -6, 4
6.9, 8.2, 9.5, 10.8
Find the next four terms of the arithmetic sequence: 3, 4.3, 5.6
1/4
Find the probability of flipping a coin 4 times and landing on heads 3 times
15/16
Find the probability of flipping a coin 4 times and landing on heads at least once
-330
Find the sum of the first 10 terms in the arithmetic series: -6 - 12 - 18 - ...
25250
Find the sum of the first 100 positive multiples of 5
5242.84
Find the sum of the first 17 terms of the series: 0.04 + 0.08 + 0.16 + 0.32 + ...
340
Find the sum of the first 8 terms in the geometric series: -4 + 8 - 16 + ...
32
Find the sum of the infinite geometric series, if possible: 8 + 6 + 9/2 + 27/8 + ...
90
I gave my friend a total of $630 over the course of seven days. Each day I gave him $10 more than the previous day. The increase in money per day stayed constant. How much money did I give on the 4th day?
60
I gave my friend a total of $630 over the course of seven days. Each day I gave him $10 more than the previous day. The increase in money per day stayed constant. How much money did I give on the first day?
200
If r = 0.2 and a₃ = 8, what is the first term of the geometric sequence?
180
If the 1st term of a geometric sequence is 500 and the 6th term is 38.88, find the 3rd term
-5
If the 2nd term of a arithmetic sequence is -15 and the 7th term is 10, find the 4th term
0.0064
In a history class, Colin and Diana both write a multiple choice quiz. There are 10 questions. Each question has 5 possible answers. What is the probability that Colin will pass the test if he guesses an answer to each question
Neither
Is the following sequence arithmetic, geometric, or neither: 1, 1, 2, 3, 5, 8
Geometric
Is the following sequence arithmetic, geometric, or neither: 1044, 522, 261
Arithmetic
Is the following sequence arithmetic, geometric, or neither: 2, 8, 14, 20
Neither
Is the following sequence arithmetic, geometric, or neither: 4, 4, 4, 4
2(a + n + 1)
Prove by induction: n² + n is even
-1/2
State the common difference/ratio. 1/3, -1/6, -2/3, -7/6
-5
State the common difference/ratio. 2, -10, 50, -250
0.605
The manufacturing sector contributes 17% of Canada's GDP. A customer orders 50 components from a factory that has a 99% quality production rate (99% of the products are defect-free). Find the probability that none of the components in the order are defective
0.089
The manufacturing sector contributes 17% of Canada's GDP. A customer orders 50 components from a factory that has a 99% quality production rate (99% of the products are defect-free). Find the probability that there are at least two defective products in the order
0.395
The manufacturing sector contributes 17% of Canada's GDP. A customer orders 50 components from a factory that has a 99% quality production rate (99% of the products are defect-free). Find the probability that there is at least one defective products in the order
0.589
The probability Time will sink a foul shot is 70%. If Tim attempts 30 foul shots, what is the probability that he sinks at least 21 shots?
0.568
The probability Time will sink a foul shot is 70%. If Tim attempts 30 foul shots, what is the probability that he sinks at most 21 shots?
0.327
The probability Time will sink a foul shot is 70%. If Tim attempts 30 foul shots, what is the probability that he sinks between 18 and 20 shots, inclusive?
0.157
The probability Time will sink a foul shot is 70%. If Tim attempts 30 foul shots, what is the probability that he sinks exactly 21 shots?
1536
The sum of the first 10 terms of a geometric series is 3069. If r = 0.5, then what is the 1st term of the series?
-236.62
The sum of the first 100 terms of an arithmetic series is 20888 and the common difference is 9. What is the 1st term?
10
Use Pascal's Triangle to find the binomial coefficient given by ₅C₂
1
Use binomial expansion to show that the following expression equals ???: (0.3 + 0.7)³
3(a + n² + n)
Use mathematical induction to prove if n ≥ 2, then n³ - n is always divisible by 3
P(1) = 0 P(n + 1) = (n + 1)(n)(n + 2) / 3
Use mathematical induction to prove the following formulas: 1(1 - 1) + 2(2 + 1) + 3(3 - 1) + ... + n(n - 1) = n(n - 1)(n + 1) / 3 when n ≥ 1
P(1) = 5 P(n + 1) = (n + 1)(n + 5)
Use mathematical induction to prove the following formulas: 5 + 7 + 9 + 11 + 13 + ... + (3 + 2n) = n(n + 1)
1.172
Use the Binomial Theorem to approximate the quantity accurate to 3 decimal places: (1.02)⁸
510568.785
Use the Binomial Theorem to approximate the quantity accurate to 3 decimal places: (2.99)¹²
4, 10, 18, 28
What are the first 4 terms of the sequence? 3n + n²
-11
What is the first term an arithmetic sequence if the 8th term is 17 and the 10th term is 25?
0
What is the sum of the first 40 terms of: -4 + 4 - 4 + 4 ...
351
What is the sum of the first 90 terms of: -5 - 4.8 - 4.6 ...
4n + 3
Write a rule for the following sequence: 7, 11, 15, 19
n - 1
Write a rule for the sequence: 0, 1, 2, 3
5n
Write an expression for the apparent nth term of the sequence: 5, 10, 15, 20, 25
17.8 - 6.5n
Write the rule/equation for the "nth" term for the sequence: 11.3, 4.8, -1.7, -8.2, -14.7
0.04
n = 10, p = 0.4, find P(1 success)
0.982
n = 100, p = 0.01, find P(no more than 3 successes)
5.526 x 10⁻⁹
n = 11, p = 0.05, find P(3 failures)
0.283
n = 12, p = 0.2, find P(2 successes)
0.043
n = 15, p = 0.9, find P(11 successes)
0.13
n = 15, p = 0.99, find P(1 failure)
0.176
n = 20, p = 0.5, find P(10 successes)
0.353
n = 6, p = 0.35, find P(at least 3 successes)
0.128
n = 7, p = 1/3, find P(4 successes)
749398
₄₁C₃₆