Arithmetic Sequences & Series
Find a formula for the arithmetic sequence 31, 23, 15, 7, ....
an = -8n + 31
The second term of a geometric sequence is -18, and the 5th term is 2/3. Find the sixth term.
-2/9
Find the coefficient a of the term in the expansion of the binomial (x + 2)^6; ax^3
160
40,320
One card is selected randomly from a standard deck of 52 playing cards. What is the probability that the card is either a club or a ten?
4/13
Write the first five terms of the arithmetic sequence if the 8th term is 26 and the 12th term is 42.
-2, 2, 6, 10, 14
Find the 10th term of the geometric sequence 6, -2, 2/3, ...
-2/6561
Find the coefficient a of the term in the expansion of the binomial (4x - y)^10; a(x^2)(y^8)
720
Twelve cyclists are competing in a race. In how many ways can the cyclists come in first, second, and third?
1320
A class is given a list of 20 study problems from which 10 will be part of an upcoming exam. If a given student knows how to solve 17 of the problems, find the probability that the student will be able to correctly answer all 10 questions on the exam?
2/19
Find the sum of the first 75 terms of the arithmetic sequence: 12n - 9
33,525
Find the sum of the first 10 terms of the geometric series (3/2)^(n-1)
58025/512
Find the coefficient a of the term in the expansion of the binomial (x - 2y)^10; a(x^8)(y^2)
180
You are dealt five cards from a standard deck of 52 playing cards. In how many different ways can you get a full house (2 of a kind & 3 of a kind)?
3744
You draw one card at random from a standard deck of 52 playing cards. Find the probability that the card is a nine or a face card.
4/13
Determine the capacity of an auditorium with 36 rows when there are 15 sets in the first row, 18 seats in the second row, 21 seats in the third row, and so on.
2430 seats
Find the infinite sum of 4(0.2)^n
5
Find the coefficient a of the term in the expansion of the binomial (2x - 5y)^9; a(x^4)(y^5)
-6,300,000
You are forming a 10-person committee from 9 women and 12 men. The committee must consist of 5 women and 5 men. How many different 10-member committees are possible?
99,792
You draw five cards at random from a standard deck of 52 playing cards. What is the probability that the hand drawn is a full house?
6/4165
In the first two trips bailing hay, around a large field, a farmer obtains 123 bales and 112 bales, respectively. Each round gets shorter, so the farmer estimates that the same pattern will continue. If he is correct, what is the total number of bales made after the farmer takes another six trips around the field?
676 bales
An investment firm has a job opening with a salary of $45,000 for the first year. During the next 39 years, there is a 5% raise each year. Find the total compensation over a 40-year period
Find the coefficient a of the term in the expansion of the binomial (3x + 4y)^8; a(x^6)(y^2)
326,592
A shipment of 25 tv sets contains three defective units. In how many ways can a vending company purchase four of these and receive 2 good units?
693
A shipment of 12 microwaves contains three defective units. A vending company purchases 4 at random. What is the probability that at least two units are good?
54/55