Sequences and Special Polynomial Products - Vocabulary (Grade 8)

Vocabulary flashcards covering key terms from sequences, arithmetic and geometric sequences, triangular and square/cube numbers, and special polynomial products.

Sequence

An ordered list of numbers formed according to a pattern or rule; each term depends on the previous term.

Finite sequence

A sequence that ends after a limited number of terms.

Infinite sequence

A sequence that continues without end.

Sequence vs. Set

A sequence is like a set but ordered; terms can repeat, while a set has no order and no repeats.

Notation for sequences

Notation such as {3, 5, 7, …} uses curly braces with comma-separated terms to denote a sequence.

Rule (in a sequence)

A rule is a method that tells how to obtain each term from previous terms.

Explicit nth-term notation

x_n denotes the nth term of a sequence.

Arithmetic sequence

A sequence in which the difference between consecutive terms is constant.

Common difference

The constant amount d added to obtain the next term in an arithmetic sequence.

Arithmetic nth-term formula

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

Example arithmetic rule

x_n = 3n − 2; generates the sequence 1, 4, 7, 10, …

Geometric sequence

A sequence in which each term is found by multiplying the previous term by a constant.

Common ratio

The constant factor r by which successive terms are multiplied in a geometric sequence.

Geometric nth-term formula

x_n = a r^(n−1), where a is the first term and r is the common ratio.

Geometric sequence notation

{a, ar, ar^2, ar^3, …} shows the pattern of terms in a geometric sequence.

Triangular numbers

Numbers formed by arranging dots in a triangle; the nth triangular number is T_n = n(n+1)/2.

Square numbers

Numbers that are perfect squares (1, 4, 9, 16, 25, …); the nth square is n^2.

Cube numbers

Numbers that are perfect cubes (1, 8, 27, 64, 125, …); the nth cube is n^3.

Square of a binomial

(a+b)^2 = a^2 + 2ab + b^2 and (a−b)^2 = a^2 − 2ab + b^2.

Sum and difference product (difference of squares)

(a+b)(a−b) = a^2 − b^2; the middle terms cancel when expanded.

Special products

A set of binomial product rules that simplify multiplication, including squares of binomials and the product of a sum and a difference.