Patterns, Sequences, General Term, & Finite Series
True or False: Linear equation for the general term is an=an2+bn+c
False: Linear equation for the general term is an=dn+b
True or False: A sequence in which any term is obtained by adding a constant to the preceding term is called an arithmetic sequence (or progression), and the constant added is called the common difference, 𝑑.
True
A geometric sequence is a sequence where each term after the first is obtained by multiplying the preceding (previous) term by a nonzero constant called the what.
common ratio
What is the Standard Fibonacci
an arrangement of numbers in which the first two terms are 1, and each term is the sum of the preceding two terms
DAILY TRIPLE
What is a Generalized Fibonacci Sequence
a sequence of numbers that begins with any two chosen starting terms—each term after the first two is obtained by adding the two terms that come before it
What equation is this used for: Sn=a1+a2+...+an
finite series
True or False: Gauss also proved the fundamental theorem of algebra, which states that every non-constant single-variable polynomial has one complex root
True
DAILY TRIPLE
What is b=± √ac used for
geometric mean
Find the first four terms of the harmonic sequence formed from the arithmetic sequence with the general term being 2n
1/2, 1/4, 1/6, 1/8
Difference Equation for Arithmetic:
A. d=(ap-aq)/(p-q)
B. d=(ap/aq)(1/p-q)
A. d=(ap-aq)/(p-q)
B is the equation for common ratio
Set or Sequence: 1, 10, 1, 10, 1, 10, ...
Sequence
insert 2 arithmetic means between 7 and 19
A.9, 13
B.10, 14
C.11, 15
D. I have no idea
C. 11, 15
d is 4 bc 19=7+3d
REVERSE (minus twice the points)
Find the 5th term of the geometric sequence:
a1=3, r=2.
48
Find the sum of the first 12 odd terms Fibonacci numbers (no need for the value u can type smth like F12)
F24 or 28657
insert 2 arithmetic means between 7 and 19
A.9, 13
B.10, 14
C.11, 15
D. I have no idea
C. 11, 15
d is 4 bc 19=7+3d
The first and the last terms of a sequence are referred to as:
A. Extremes
B. Means
C. General Term
A. Extremes
DAILY DOUBLE
What is Gauss known as what
Prince of Mathematicians
Difference Equation for Geometric:
A. r=(ap-aq)/(p-q)
B. r=(ap/aq)(1/p-q)
B
A sequence is defined by F1=2, F2=3, and Fn=Fn−1+Fn−2 for n≥3. Find the 8th term.
F8=55
REVERSE (minus twice the points)
True or False: Harmonic Sequence can have 0 as a term
No bc the arithmetic would need to have 1/0 as a term and 1/0 is undefined
Is this finite or infinite:
1, 2, 3, 4, 5, ..., 10, 11, ..., 100
finite
Difference Equation for Arithmetic:
A. d=(ap-aq)/(p-q)
B. d=(ap/aq)(1/p-q)
A. d=(ap-aq)/(p-q)
B is the equation for common ratio
Determine the 8th term and the sum of the first 8 terms of the sequence:
a1=2, r=−3.
a8=−4374
S8=−3280
DAILY DOUBLE
True or False: Harmonic Sequence can have 0 as a term
No bc the arithmetic would need to have 1/0 as a term and 1/0 is undefined
a German polymath renowned as the “Prince of Mathematicians” for his profound and wide-ranging contributions to mathematics and science
A. Rene Descartes
B. Carl Friedrich Gauss
C. Leonardo Fibonacci
B. Carl Friedrich Gauss