Classifying Sequences
Is the sequence below arithmetic, geometric, or neither? State the growth factor or rate of change, if applicable. {1, 2, 3, 4, 5, ...}
Arithmetic, rate of change: 1
Write a recursive formula for the following sequence: {30, 26, 22, 18, ...}
f(1)=30, f(n)=f(n-1)-4
Write a definition for the nth term for the sequence below: {6, 11, 16, ...}
f(n)=6+5n
A sequence is defined by f(1)=6, f(n)=3f(n-1) . Which of the following defines the nth term of f ?
A) f(n)=6\cdot3^n, n>=0
B) f(n)=6\cdot3^(n-1), n>=1
Is the sequence below arithmetic, geometric, or neither? State the growth factor or rate of change, if applicable. {20, 15, 10, ...}
Arithmetic, rate of change: -5
Write a recursive formula for the following sequence: {3, 9, 27, 81, ...}
f(1)=3, f(n)=f(n-1)\cdot 3
Write down the first 4 terms of the sequence defined by: f(1)=2, f(n)=f(n-1)\cdot 4
2, 8, 32, 128
A sequence is defined by f(1)=-1, f(2)=-2, f(3)=-3, f(4)=-4 . Write down a recursive definition for this sequence.
f(1)=-1, f(n)=f(n-1)-1
Is the sequence below arithmetic, geometric, or neither? State the growth factor or rate of change, if applicable. {1, 4, 9, 16, ...}
Neither
Write a recursive formula for the following sequence:
{ 1, 3/4, 9/16, 27/64 }
f(1)=1, f(n)=f(n-1)\cdot 3/4
A sequence is defined by
f(0)=50, f(1)=30, f(2)=10, f(3)=-10
Write the explicit formula for the sequence?
f(n)=50-20n
A sequence begins with g(1)=2, g(2)=10 . Write down a definition for the nth term if g is a geometric sequence.
g(n)=2\cdot5^n
Is the sequence below arithmetic, geometric, or neither? State the growth factor or rate of change, if applicable. { 20, 20/3, 20/9 }
Geometric, growth factor:
1/3
Write a recursive formula for the following:
{ -1/2, 1/2, -1/2, 1/2, ... }
f(1)=-1/2, f(n)=f(n-1)\cdot -1
Write down the first 4 terms of the sequence defined by: f(n)=120\cdot(1/4)^n
120, 30, 7.5, 1.875
Write down the first 4 terms for the sequence: f(1)=1, f(n)=3f(n-1)+1
1, 4, 13, 40
Is the sequence below arithmetic, geometric, or neither? State the growth factor or rate of change, if applicable. {0.1, 0.01, 0.001, ...}
Geometric; growth factor 0.1
Write a recursive formula for the following sequence:
{ 1, 3/4, 1/2, ... }
f(1)=1, f(n)=f(n-1)-1/4
A sequence is given by f(1)=-1, f(n)=f(n-1)+4 . Write down two equivalent definition for the nth term, one where we assume we begin at 0 and one where we assume we begin at 1.
f(n)=-1+4n, n>=0
f(n)=-1+4(n-1), n>=1
Write down the first four terms of this sequence.
f(1)=3, f(n)=f(n-1)^2-1
3, 8, 63, 3968