Arithmetic Sequences & Series
Find the common difference and the first 5 terms of the following arithmetic sequence:
{a_n} = {16 - 1/2n }
d = -1/2 ; a_1 = 15.5, a_2= 15, a_3 = 14.5, a_4 = 14, a_5 = 13.5
Find the sum:
sum_(k=1)^10 (-2)^k
682
Expand and simplify: (x + 1)3
x3 + 3x2 + 3x + 1
Find the values of: 8C3 and 8P3
8C3 = 56; 8P3 = 336
Construct a probability model for the experiment: tossing a fair coin, then a fair die.
{H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}; each probability = 1/12
Find the 80th term of: 5, 0 , -5, ...
-390
Find the 10th term of the geometric sequence:
1, -2, 4, ...
-512
Expand and simplify: (2x + 3)4
16x4 + 96x3 + 216x2 + 216x + 81
In how many ways can a squad of 4 relay runners be chosen from a track team of 8 runners?
1,680 ways
Two fair 6-sided dice are rolled. What is the probability of rolling a sum of 6 or a sum of 8?
10/36 = 5/18
Find the sum of: 5 + 9 + 13 + ... + 49
324
Find the nth term formula of a geometric sequence whose 3rd term is 100 and 6th term is 12.5. Make sure to simplify your final answer.
{ a_n } = { 400(1/2)^(n-1) }
Expand and simplify: (x2 + 5y)3
x6 + 15x4y + 75x2y2 + 125y3
How many different 11-letter words (real & imaginary) can be made from the word MISSISSIPPI?
(11!)/(4!4!2!) = 34,650
On "The Price is Right" there is a game in which a bag is filled with 3 strike chips and 5 numbers. Let's say that the numbers in the bag are 0, 1, 3, 6, and 9. What is the probability of selecting a strike chip or the number 1?
3/8 + 1/8 = 4/8 = 1/2
Find the nth term formula of an arithmetic sequence whose 5th term is -2 and 13th term is 30. Make sure to simplify your final answer.
{a_n} = { 4n - 22 }
Determine if the following infinite geometric series converges or diverges. If it converges, find its sum.
2 - 1 + 1/2 - 1/4 + ...
converges
S_\infty = 4/3
Expand and simplify: (2x2 - y2)5
32x10 - 80x8y2 + 80x6y4 - 40x4y6 + 10x2y8 - y10
A license plate consists of 1 letter, excluding O and I, followed by a 4-digit number that cannot have a 0 in the lead position. How many different plates are possible?
216,000 different plates
The faculty of a math department at a local college is composed of 4 females and 9 males. Of the 4 females, 2 are under the age of 40; and of the males, 3 are under the age of 40. What is the probability that a randomly selected faculty member is male or over the age of 40?
11/13
An outdoor amphitheater has 35 seats in the first row, 37 in the second row, 39 in the third row, and so on. There are 27 rows altogether. How many people can the amphitheater seat?
1,647 seats/people
Find x so that x + 2, x + 3, and x + 5 are consecutive terms (in that order) of a geometric sequence.
x = -1
Find the 5th term of (3x2 - 4y2)7
241,920x6y8
A combination lock displays 50 numbers. To open it, you turn to a number, then rotate clockwise to a second number, and then counterclockwise to a third number. How many different lock combinations are there?
125,000 if you can turn back to the same number; 117,600 if you cannot turn back to the same number
What is the probability that at least 2 people have the same birthday in a group of 12 people? Assume that there are 365 days in a year.
0.167