Algebra II U1L10&11

A recursive definition defines a sequence in terms of itself, using previous terms to calculate subsequent terms.

The base case is the initial term of the sequence that does not depend on previous terms, providing a starting point for the recursion.

A sequence is an ordered list of numbers, where each number is called a term.

The nth term of a geometric sequence can be defined as $$a_n = a_1 \times r^{(n-1)}$$ , where $$a_1$$ is the first term and $$r$$ is the common ratio.

The nth term of an arithmetic sequence can be defined as $$a_n = a_1 + (n-1)d$$ , where $$a_1$$ is the first term and $$d$$ is the common difference.

The common difference is the constant amount that each term increases or decreases by in an arithmetic sequence.

The common ratio is the constant factor by which each term of a geometric sequence is multiplied to get the next term.

Start with the base case and use the recursive formula to calculate each subsequent term.

The notation $$g(n)$$ represents the nth term of the sequence g, where n is a positive integer.

It signifies that the first term of the sequence g is 200.