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Sequences
Series (AKA Sum)
Permutation/Combination
Unit Circle Returns...
Word Problems
100
What is the formula for the nth term of a geometric sequence?
An = A1*r^(n-1)
100
What is the equation to find the nth partial sum of an arithmetic sequence?
Sn = (a1+an)*n/2
100
Identify n and r in the following problem: There are 35 boys trying out for football in the fall. The coach only has 20 spots to fill on the roster. How many ways can he fill the remaining spots?
n = 35 and r = 20
100
What is cos(0)?
1
100
Joe averaged 123 total pins per game in his bowling league this season. He is taking bowling lessons and hopes to bring his average up by 8 pins each new season. Write an equation to represent the nth term of the sequence.
An = 123 + 8(n-1)
200
Find the 3rd term of the recursive sequence: a1 = 4 ak+1 = ak - 5
-6
200
Find the sum of the following sequence: 1, 2, 3, 4, 5, 6....111, 112, 113, 114
6555
200
There are 53 concert choir members going on a field trip. How many ways can Mr. Doughty put them in groups of two for the bus ride?
1378 ways
200
What are the coordinates of pi/3?
(1/2, sqrt3/2)
200
Sarah receives a joke in an e-mail that asks her to forward it on to four of her friends. She forwards it, then each of her friends forwards it to four of their friends, and so on. If the pattern continues, how many people will receive the e-mail on the ninth round of forwarding?
262,144 people
300
Find the 20th term of the arithmetic sequence 9, 16, 23, 30,... using the nth term equation.
142
300
Find the sum of the following sequence: 3, 12, 48, ... , 196608
262,143
300
To open your locker, you must dial a sequence of three numbers called the lock’s combination. Given that there are 40 numbers on a lock, how many different locker combinations are there?
59,280 combinations
300
What is the sine of 63pi/2?
-1
300
Cans are stacked in a display of rows with 1 can in the top row, 4 cans in the second row, 7 cans in the third row and so on. If there are 298 cans in the bottom row, how many cans total are there in the display?
14,950 cans
400
Find An for the geometric sequence in which A1 = 800, r = 1/2, n = 6.
25
400
The 2nd term of an arithmetic sequence is 9. The 5th term is 21. Find the sum of the first six terms.
90
400
An expanded ZIP code, called ZIP+4, is composed of the original five-digit code plus a four-digit add-on code. Find the number of ZIP codes consisting of five digits followed by the four additional digits when the first number of the five-digit code is 1 or 2 and the last digit of the four-digit code is odd.
100,000,000 ZIP codes
400
Solve the trigonometric equation and find the general solution(s): 2cosxsinx + sinx=0
0,pi + 2pi*n 2pi/3, 4pi/3 + 2pi*n
400
A new shoe company sold $10,000 worth of product in their first month. They believe they will increase sales by 15% each month over their first year. If this increase does occur what will be the total sales for the company in their first year?
$290,016.67
500
Write an explicit formula and a recursive formula for the sequence 4, 10, 25, 62.5,...
Explicit: an = 4*2.5^(n-1) Recursive: a1 = 4, an+1 = an*2.5
500
The 2nd term of a geometric sequence is 1024 and the 6th term is 64. Find the sum of the first 20 terms of the sequence to three decimal places.
4095.996
500
A six-member math team is to be formed having one administrator, three faculty members, and six students. There are five administrators, twelve faculty members, and 25 students in contention for the math team. How many six-member math teams are possible?
194,810,000 six-member math teams
500
What are the solutions to the equation csc(2x) = sqrt(2) on the interval [0, pi)?
pi/8 and 3pi/8
500
Susan started a new running program... on May 1st she ran 0.2 miles. Her plan each day is to double the amount she ran the day before. How many total miles will she run during the month of May? (There are 31 days in the month of May.)
429,496,729.4 miles