Ch.9 Sequences and Series

Section 2 – Arithmetic Sequences

Definition: Arithmetic Sequence

A sequence where the difference between consecutive terms is constant. This difference is the common difference.

a, a + d, a + 2d, a +3d,…

Formulas

Recursive: initial conditionrecursive formula

Explicit:

EXamples

Is the sequence an arithmetic sequence?1.) 3,6,9,12,15,…

2.) 1,4,9,16,25,…

EXamples

What is the 100th term of the sequence beginning with 6, 11, …?

EXample

What are the second and third terms of the arithmetic sequences 100, __, __, 82,…

Definition: Arithmetic Mean

The average of two numbers and .

In an arithmetic sequence, the middle term of any three consecutive terms is the arithmetic of the other two terms.

EXample

What is the missing term of the arithmetic sequence …, 15, __, 59, …?

EXample

The numbers of seats in the first 13 rows in the section of an arena form an arithmetic sequence. Row 1 has 14 seats, row 2 has 16 seats. How many seats are in row 13?