Special Sequences Flashcards

A sequence where each term is found by adding or subtracting the same value (common difference) to the previous term.

A sequence where each term is found by multiplying or dividing the previous term by the same value (common ratio).

A sequence where each term is the sum of the two previous terms, starting with 0 and 1 (e.g., 0, 1, 1, 2, 3, 5, 8...).

A sequence of numbers that can form an equilateral triangle (e.g., 1, 3, 6, 10, 15...). The nth term is given by n(n+1)/2.

A sequence of numbers obtained by squaring integers (e.g., 1, 4, 9, 16, 25...). The nth term is n².

A sequence of numbers obtained by cubing integers (e.g., 1, 8, 27, 64, 125...). The nth term is n³.

The nth term of an arithmetic sequence is given by a + (n-1)d, where a is the first term and d is the common difference.

The nth term of a geometric sequence is given by ar^(n-1), where a is the first term and r is the common ratio.

A sequence of numbers where each term is an even integer (e.g., 2, 4, 6, 8, 10...). The nth term is 2n.

A sequence of numbers where each term is an odd integer (e.g., 1, 3, 5, 7, 9...). The nth term is 2n-1.