Arithmetic and Geometric Sequences

These flashcards cover key concepts related to arithmetic and geometric sequences, including formulas and methods for finding specific terms in the sequences.

In an arithmetic sequence, the common difference (d) is added to the previous term to find the next term. For example, if the first term is -8 and the common difference is 5, the 5th term can be found using the formula __.

An = a + (n-1)d.

In a geometric sequence, each term is found by multiplying the previous term by a common ratio (r). For example, to find the 5th term with the first term a = 5 and common ratio r = 5, you would use the formula __.

Gn = a * r^(n-1).

The formula for finding any term in an arithmetic sequence is __.

A = a + (n-1)d.

In a geometric sequence, if the first term is 5 and the common ratio is 5, the 12th term is __.

G12 = a * r^(12-1) = 5 * 5^(11).

The first term in the given arithmetic sequence is __.

-8.

To find the 100th term of the arithmetic sequence with first term -8 and common difference 5, you would calculate __.

A = -8 + (99)(5) = 487.

The term for the next value in an arithmetic sequence can be calculated as __ the previous term.

the previous term + d.

For a geometric sequence with terms 25, 125, 625, the common ratio r is __.

5.