Arithmetic and Geometric Sequences
Sequences and Series
Binomials
Probability
Random
100
Part 1:
What is the formula for finding the sum of a finite geometric sequence (standard formula) ?
Part 2:
What restriction must be true to find the sum of infinitely many? What is the new formula?
Part 1:
Sn = (a1 (1-rn))/ 1-r
Part 2:
Restriction: lrl<1
Formula: Sn= a1/ 1-r
100
Write the first five terms of the sequence
an = 10n + 3
(assume that n begins with 1)
a1= 13
a2= 23
a3=33
a4=43
a5=53
100
Use the binomial theorem to expand and simplify the expression
(a+5)3
a3 + 15a2 + 75a + 125
100
There is a spinner with 15 equal areas, numbered 1 through 15. If the spinner is spun one time, what is the probability that the result is a multiple of 6 or a multiple of 4?
4/15 probability
100
Identify these two sequences:
1)
2)
1)Probability of independent events
2) Probability of Dependent Events
200
Consider a1=-6, d=-5 and n= 9
What type of sequence is this and what is the nth term?
1) Arithmetic
2)-46
200
Write the first five terms of the sequence
an = (-3)n+1
(Assume that n begins with 1)
a1= 9
a2=-27
a3=81
a4=-243
a5=729
200
Find the specified nth term in the expansion of the binomial
(a+b)7 n= 4
35a4b3
200
A bag contains 3 red marbles, 7 blue marbles and 8 green marbles. If three marbles are drawn out of the bag, what is the exact probability that all three marbles drawn will be green?
7/102
200
Use sigma notation to write the sum:
5+12+19+26+33+40+47+54
300
Find the first 5 terms of the geometric sequence with a1 = 6 and r = -0.2
6,-1.2,0.24,-0.048,0.0096
300
Write an expression for the apparent nth terms (an) of the sequence
3,7,11,15,19
(Assume that n begins with 1)
an= 3+4(n-1)
OR
an=4n-1
300
Use the binomial theorem to expand and simplify the expression
(x+2y)3
x3 + 6x2y + 12xy2 + 8y3
300
In a class of students, the following data table summarizes how many students passed a test and complete the homework due the day of the test. What is the probability that a student chosen randomly from the class did not complete the homework?
5/23
300
Find the Sum
80
400
Find Sn for the series
160+80+40+... n=11
USE THIS FORMULA:
Sn = (a1(1-rn))/ 1-r
Answer: 10235/32 or 319.84
400
Write an expression for the apparent nth terms (an) of the sequence
2/1, 3/3, 4/5, 5/7, 6/9
(Assume that n begins with 1)
an= n+1/2n-1
400
Use the binomial theorem to expand and simplify the expression
(3y-4x)5
243y5 - 1620y4x + 4320y3x2 - 5760y2x3 + 3840yx4 -1024x5
400
In a class of students, the following data table summarizes the gender of the students and whether they have an A in the class. What is the probability that a female student does not have an A?
5/8
400
Evaluate these two expressions:
1)
2)
1)220
2)5040
500
Find Sn for the series
60+46+32+18... n=15
a15= -136
S15= -570
500
write the first five terms of the sequence
an = 2/3
(assume that n begins with 2)
a2= 2/3
a3= 2/3
a4= 2/3
a5= 2/3
a6=2/3
500
Find the specified nth term in the expansion of the binomial
(10x+3y)6 n= 4
540000x3y3
500
In a class 18 of students, 11 have a cat and 12 have a dog. There are 4 students who do not have a cat or a dog. What is the probability that a student chosen randomly from the class has a cat or a dog?
7/9
500
The menu for afternoon tea at Peet’s Coffee consists of the following:
6 options for coffee
4 options for cake
3 options for foodstuff
You decide to order afternoon tea with a budget of $9.95, which allows you to pick two different coffees, one slice of cake and one foodstuff. How many possible menu combinations are available for $9.95?
180 possible combinations