A Sequence of Unfortunate Events
This is the name for the famous sequence that can be written as "an=an-1+an-2"
What is the Fibonacci Sequence?
(0, 1, 1, 2, 3, 5, 8, 13, 21, ...)
ln(n) is equal to this where "n" is the smallest prime number (round to the nearest hundredth).
What is 0.69?
This is the likelihood of rolling an even number on a 6-sided die three times in a row?
What is "1/8" or "0.125"?
(1/2)*(1/2)*(1/2)=1/8
These are the first 5 digits of pi
3.1415
Complete the following sequence
0, 1, 1, 4, 9, 25, 64, 169, __
What is 441?
The sequence is the Fibonacci sequence with each term squared
02, 12, 12, 22, 32, 52, 82, 132, __212___
212 = 441
This is the first 3 digit prime?
101
This is the likelihood of drawing a red face card from a regular 52-card deck (must be simplest form).
Face cards include Jacks, Queens, and Kings
What is "3/26" or "0.115"?
What are the first three digits of e (rounded)?
What is "2.72"?
This is the next number in the sequence
1, 11, 21, 1211, 111221, 312211, ___
What is 13112221?
This is known as the "Look-and-Say" Sequence where you quite literally say the numbers you see and write it out. For example, the first term is "one 1" which becomes "11," then that is "two 1" which is "21" and so on.
This is the sum of all even prime numbers less than 100.
2
2 is the only even prime number
Given that a child rolls a normal 6-sided dice and a tetrahedron (4-sided dice), this is the likelihood of rolling the same number on each die within a single roll.
What is "1/6" or "16.67%"?
Order the following from least to greatest:
▪ i16
▪ i54
▪ e*(i48)
What is "i54 < i16 < e*(i48)"?
If the sum of 15 consequtive integers is 2025, then this is the sum of the integers with only odd digits.
What is 675?
2025 = x+(x+1)+(x+2)+...+(x+13)+(x+14)
= 15x+(1+2+...+13+14)
= 15x+(14[14+1]/2) = 15(x+7)
x+7 = 2025/15 = 135
128 ≤ x ≤ 142
The only integers in this range with odd digits are 131, 133, 135, 137, and 139 which have a sum of 675
There are this many prime numbers less than or equal to 67.
What is 19?
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67
Given the information that a couple has two kids. This is the likelihood that the first child is a boy and the second child was born on a Tuesday.
What is "1/14" or "7.14%"?
This is the error for the following equation:
(ax+by)2 = (ax)2+2(a+b)xy+(by)2
What is the second term on the righthand side of the equation should be "2(ab)xy", bit "2(a+b)xy"?
For the sequence "17, 16, 20, 11, 27, 2, 38, ..." the next term has this value.
What is -11?
an = an-1+(n-1)2(-1)n+1 {a1=17}
a8 = a7+72(-1)9 = 38-49 = -11
There are this many distinct primes in the prime factorization of 2026
(Prime factorization is breaking a number down into all of its primes. For example, 210 would be 2*3*5*7 and have 4 distinct primes)
What is 2?
2 and 1013
Given the following information, there are this many girls who earned an A the exam:
▪ 116 students take an exam
▪ 1/4 of girls and 1/7 of boys earn an A
▪ 23 students earn an A
What is 15?
G+B=116; G/4+B/7=23
3B/7=24, therefore B=56 and G=60
Since 1/4 of girls passed the exam, 15 girls passed
Identify which one(s) of the following equations is/are incorrect and what the correct answer(s) are:
▪ ln(e4) = 4
▪ cos(x+ℼ) = -cos(x)
▪ sec2(x)+tan2(x) = sin2(x)+cos2(x)
Incorrect: sec2(x)+tan2(x) = sin2(x)+cos2(x)
Should Be: sec2(x)-tan2(x) = sin2(x)+cos2(x)