Algebra 2: Arithmetic & Geometric Sequences Flashcards
What operations do Arithmetic sequence cover?
Addition and Subtraction
What is a sequence?
An ordered list of numbers, each being a term in the sequence. The numbers can follow a pattern (common difference or constant ratio).
What is a series?
An expression formed by adding the terms of a sequence.
What are the variables in an arithmetic sequence and what do they stand for?
a: first term
d: common difference
n: term number
Explicit formula for an arithmetic sequence starting at zero:
f(n) = a + d(n)
n>= zero
Recursive formula for an arithmetic sequence starting at zero:
f(0) = a
f(n) = f(n-1) + d
n>=1
“previous term plus common difference”
Explicit formula for an arithmetic sequence starting at one:
f(n) = a + d(n-1)
n >=1
“first term + (common difference x the previous term)”
Recursive formula for an arithmetic sequence starting at one:
f(1) = a
f(n) = f(n-1) + d
n>=2
“previous term plus common difference”; SAME AS AT ZERO
What operations do Geometric sequences cover?
Multiplication and Division
What are the variables in geometric series and what do they stand for?
a: first term
r: constant ratio
n: term number
What can ‘r’ in a geometric series NOT equal?
1
Explicit formula for a geometric sequence starting at zero:
f(n) = a * (r^n)
n>=0
Recursive formula for a geometric sequence starting at zero:
f(0) = a
f(n) = r * f(n-1)
n>=1
“previous term times constant ratio”
Explicit formula for a geometric sequence starting at one:
f(n) = a * (r^n-1)
n>=1
Recursive formula for a geometric sequence starting at one:
f(1) = a
f(n) = r * f(n-1)
n>=2
“previous term times constant ratio”; SAME AS AT ONE
