Arithmetic Sequences/Series
Find the formula that represents the nth term of the following sequence:
5, 11, 17, ...
6n - 1
or
5 + 6(n-1)
Write a formula that represents the nth term of the following sequence:
20, 5, 1.25, ...
20(1/4)n-1
How many different outfits can you make from your closet if you have 10 different shirts, 4 different pairs of pants, and 7 different pairs of shoes if each outfit consisted of one shirt, one pair of pants, and one pair of shoes?
280
What is the probability of selecting a spade that is not a face card and not an ace from a standard deck of 52 playing cards?
9/52 or .173
How many terms are in the following sequence?
9, 12, 15, ..., 159
51
Find a10 of the following sequence:
-2, -8, -32, ...
-524,288
How many different ways can 16 movies be arranged on a shelf, taking 8 movies at a time?
518,918,400
A 12-sided die is rolled twice. What is the probability of rolling doubles (the two faces are the same number)?
1/12 or .0833
Find the sum of the first 15 terms of the following sequence:
29, 25, 21, ...
15
Find the sum of the first 7 terms of the following sequence:
9, 3, 1, ...
1093/81
or
13.5
In a high school where there are 50 students and 22 are girls, how many different ways can the student council of 5 people be chosen if the council must consist of exactly 2 girls and 3 boys?
756,756
One card is selected at random from a standard deck of 52 playing cards. What is the probability that the card chosen is either a 7 through 10, OR a diamond?
25/52 or .481
Find the 20th term of the sequence where a5 = 34 and a9 = 58.
Find the sum of the following series:
3, -6, 12, -24, ...
No sum!
In a high school where there are 50 students and 22 are girls, how many different ways can the president, vice president, and secretary of the student council be chosen if AT LEAST one of those positions has to be a girl, but the other two positions could also be filled by girls?
51744
A woman has 22 pairs of shoes (no two pairs are the same). In the dark, she randomly selects two shoes from her closet. What is the probability that those two shoes are a matching pair?
1/21 or 22/462 or .048
Expand (2x - 3y)6.
64x6 - 576x5y + 2160x4y2 - 4320x3y3 + 4860x2y4 - 2916xy5 + 729y6