Sequences and Series

These flashcards cover key terms and definitions related to sequences and series, including arithmetic and geometric progressions, as well as concepts of convergence and divergence.

Sequence

A set of numbers where consecutive terms are connected by a definite rule or pattern.

Series

The sum of the terms of a sequence.

Finite Sequence

A sequence that consists of a countable number of terms, specified by a complete list.

Infinite Sequence

A sequence that consists of an infinite number of terms, indicated by three dots after the last term.

Arithmetic Progression (AP)

A series where each term is obtained from the preceding one by the addition of a constant quantity, known as the common difference.

Common Difference

The constant quantity added to each term in an arithmetic progression.

nth Term

The term in a sequence that corresponds to the position n.

Geometric Progression (GP)

A series where each term is obtained from the preceding one by the multiplication of a constant quantity, known as the common ratio.

Convergent Series

A series whose terms approach a fixed limit as more terms are added.

Divergent Series

A series whose terms do not approach a fixed limit as more terms are added.

Σ Notation

A way to denote the sum of a sequence of terms.

Sum of the first n terms of an AP

Calculated using the formula S_n = n/2 (a + l), where a is the first term, l is the last term, and n is the number of terms.

Sum to Infinity of a GP

Exists only when the common ratio r is less than 1, calculated using the formula S = a / (1 - r).

Common Ratio

The constant quantity multiplied to obtain each successive term in a geometric progression.

nth Term Formula of an AP

T_n = a + (n−1)d, where a is the first term and d is the common difference.