Arithmetic Sequences Basics A sequence is a list

Arithmetic Sequences

Basics… • A sequence is a list of numbers that may form a pattern. Each number in a sequence is called a term. • When the terms of a sequence differ by the same nonzero number (any number except 0) d, the sequence is an arithmetic sequence and d is the common difference.

Formula 1

Example 1: Determine whether each sequence is an arithmetic sequence. If so, find the common difference and the next three terms. •

Example 2: Determine whether each sequence is an arithmetic sequence. If so, find the common difference and the next three terms. •

Practice… •

Formula 2 We use this formula to find ANY number in the sequence.

Example 4: Find the indicated term in each arithmetic sequence. •

Example 5: Find the indicated term in each arithmetic sequence. •

Practice… •

Geometric Sequences

Basics… • In a geometric sequence, the ratio of successive terms is the same number r, called the common ratio.

Example 1: Find the next three terms in the geometric sequence. •

Example 2: Find the next three terms in the geometric sequence. •

Formula an = a 1 rn– 1 nth term 1 st term Common ratio

Example 3: Find the nth term of a Geometric Sequence. • an = a 1 rn– 1

Example 4: Find the nth term of a Geometric Sequence. • an = a 1 rn– 1

Example 5: Find the nth term of a Geometric Sequence. • an = a 1 rn– 1

Example 6: Find the nth term of a Geometric Sequence. • an = a 1 rn– 1

Homework • Homework: Page 209 (10 -20 even, 22 -30 even) • Homework: Page 621 (2, 3, 5, 8, 9, 11, 12, 14)