SWBAT…write terms of an arithmetic sequence Tues, 4/17

Agenda 1. WU (10 min)2. Notes on arithmetic sequences: 7 examples (35 min)

Warm-Up:

1. Set up your Cornell notes. Topic is “Arithmetic Sequences.”

2. What pattern do you notice 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, . . . .

HW: Arithmetic Sequences

Fibonacci Sequence

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, . . .

A sequence is a list of numbers that are related to each other by a rule.

The numbers in a sequence are called its terms.o The letter a with a subscript is used to represent the terms

of a sequence.o a1 represents the first term of the sequenceo a2 represents the second term of the sequenceo a3 represents the third term of the sequence, and so on

If the difference between successive terms is constant, then the sequence is called an arithmetic sequence.

The difference between consecutive terms is called the common difference, d, of the sequence.

To find the common difference (d), subtract any term from one that follows it.

2 5 8 11 14

1a 2a 3a 4a 5a

3 3 3 3

Example 1Write the first six terms of the arithmetic sequence with the first term 6 and common difference 4.

Solution6, 10, 14, 18, 22, and 26

Example 2Write the first six terms of the arithmetic sequence with a1 = 5 and d = -2.

Solution5, 3, 1, -1, -3, and -5

Find the first term and the common difference of the arithmetic sequence.

34, 27, 20, 13, 6, -1, -8, …

Solution:First term: 34

Common difference (d): = 27 – 34 = -7

The nth term of an arithmetic sequence with first term a1 and common difference d is:

1 ( 1)na a n d The value of the term you are looking for

First term

The position the term is in The common

difference

Find the eighth term of the arithmetic sequence whose first term is 4 and whose common difference is -7.

1 ( 1)na a n d

Example 4

a8 = 4 + (8 – 1)(-7)

a8 = 4 + (7)(-7)

a8 = -45Check this result by writing the first eight terms of the sequence:

a8 = 4 + (-49)

4, -3, -10, -17, -24, -31, -38, -45

Find the 14th term of the arithmetic sequence 4, 7, 10, 13,…

1 ( 1)na a n d 14a (14 1) 4 3

4 (13)3 4 39 43

Example 5

1 ( 1)na a n d

In the arithmetic sequence 4, 7, 10, 13,…, which term has a value of 301?

301 4 ( 1)3n 301 4 3 3n 301 1 3n 300 3n100 n

Example 6

Find the formula for the nth term of the arithmetic sequence -7, -4, -1, 2…

A. an = 3n – 4

B. an = -7n + 10

C. an = 3n – 10

D. an = -7n + 4

Example 7