Sequences and Series

Flashcards for review of arithmetic and geometric sequences, series, and finance problems.

Arithmetic Sequence

A sequence where the difference between consecutive terms is constant.

Arithmetic Sequence (explicit formula)

an = a₁ + (n-1)d

Geometric Sequence

A sequence where each term is multiplied by a constant ratio to get the next term.

Geometric Sequence (explicit formula)

an = a₁ * r^(n-1)

Recursively-defined Sequences

Sequences defined by a formula that relates each term to the previous term(s).

Arithmetic Recursive Formula

an = a(n-1) + d

Geometric Recursive Formula

an = a(n-1) * r

Arithmetic Series

The sum of the terms in an arithmetic sequence.

Arithmetic Series Formula

Sn = (n/2) * (a₁ + an)

Geometric Series

The sum of the terms in a geometric sequence.

Geometric Series (finite) Formula

Sn = a₁ * (1-r^n) / (1-r), when r≠1

Infinite Geometric Series

The sum of an infinite geometric sequence, when |r| < 1.

Infinite Geometric Series Formula

S = a₁ / (1-r), when |r| < 1

Sigma Notation

A notation used to represent the sum of a series.

Σ notation (∑a_i from i=1 to n)

Represents the sum of terms a_i from i=1 to n.

Compound Interest Formula

A(t) = P(1 + r/n)^(nt)

A(t)

Amount after t years

P

Initial amount (Principal)

r

Annual interest rate

n

Number of times interest is compounded per year