General Sequences and Series
Arithmetic Sequences
Geometric Sequences
Arithmetic Series
Geometric Series
Pot Luck
100
What is the difference between a sequence and a series?
A sequence is an ordered list of numbers, whereas a series is the sum of a given number of terms in a sequence.
100
What does the acronym "btw" stand for?
"by the way"
100
For the given sequence, find the common ratio and the 9th term:
1/2, 2, 8, ...
r = 4
a12 = 32,768
100
Find S9
13, 15, 17, ...
S9 = 189
100
Find S7 for the following sequence:
-2, -12, -72, ...
S7 = -3110
100
What is the rule for the sum to infinity?
a/(1-r)
200
What is the difference between an arithmetic and a geometric sequence?
An arithmetic sequence is a sequence that has a common difference (the same number gets added each time).
A geometric sequence is a sequence that has a common ratio (the same number gets multiplied each time).
200
Given that a1 = 7 and an = an-1 - 3, find a6.
a6 = -8
200
How many Harry Potter books and movies are there?
7 books, 8 movies
200
Evaluate the given series.
S10 = 365
200
Evaluate the given series:
S9 = 39,364
200
For the sequence un=cos(90n), what type of sequence would this be?
Periodic, order 4
300
Given a1 = 2 and an = 4an-1 + 1, find a5.
a5 = 597
300
For the given sequence, find the common difference and the 10th term.
9, 12, 15, 18, ...
d = 3
a10 = 36
300
Given that a1 = -5 and an = 2an-1, find a6.
a6 = -160
300
Who sings the song "Say So"?
Doja Cat
300
Find the infinite sum, if possible.
1 + 0.5 + 0.25 + ...
2
300
For the function f(x)=(4x)^2 + 5, calculate f(10)
1605
400
There are 130 students in grade 1, 210 students in grade 2, and 290 students in grade 3 in a primary school, and so on in an arithmetic sequence. What's the total amount of students in the school? (there are 6 grades in the school).
1980 students
400
Find three arithmetic means between -3 and 29.
5, 13, 21
400
Find two geometric means between 6 and 162.
18, 54
400
Evaluate the following series:
a1 = 42, an = 146, n = 14
1316
400
What day is Star Wars day?
400
What university did Mrs Barnes study at?
Exeter
500
What singer holds the record for the most Grammy nominations?
Beyonce
(She has a total of 88 nominations!)
500
Given the explicit formula below, find the first four terms and a15.
an = -11+(n-1)7
-11, -4, 3, 10
a15 = 87
500
Given the explicit formula below, find the first four terms and a10 (round to nearest thousandth).
an = (1200)(1/2)n-1
1200, 600, 300, 150
a10 = 2.344
500
Determine the number of terms in the series:
-1 + 2 + 5 + ... + 68
n = 24
500
Find the infinite sum, if possible.
a1 = -3, r=4
No sum (diverges)
500
Find the inverse function of f(x)=(x+1)/(x-3)
(1-3x)/(x-1)