Pg. 417/425 Homework

• Pg. 395 #43, 60Pg. 589 #1 – 8 all, 17, 18, 21, 22

11.1 Sequences

Finding Terms in a Sequence• List the first three terms and

the 15th term of the following sequences:

Fibonacci Sequence• 0, 1, 1, 2, … do you

know/see a pattern?• an = an – 1 + an – 2 • Find the first 15 terms of

the Fibonacci Sequence.

2 1n

na

n

1 2n n

nb

11.1 Sequences

Arithmetic Sequences

• A sequence {an} is called an arithmetic sequence if there is a real number d such that:

and

for every positive integer n.

• The number d is called the common difference of the arithmetic sequence.

• What do the subscripts mean?

• How are these two formulas different from each other?

1n na a d

1 1na a d n

11.1 Sequences

Examples• The first two terms of an

arithmetic sequence are -8 and -2. Find the 10th term and a formula for the nth term.

• The third and eighth terms of an arithmetic sequence are 13 and 3, respectively. Determine the 1st term and the nth term.

11.1 Sequences

Geometric Sequences

• A sequence {an} is called an geometric sequence if there is a nonzero real number r such that:

and

for every positive integer n.

• The number r is called the common ratio of the geometric sequence.

• How are these two formulas different from each other? 1n na r a

11n

na a r

11.1 Sequences

Examples• The second and third terms

of a geometric sequence are -6 and 12, respectively. Determine the 1st term and the formula for the nth term.

• The second and third terms of a geometric sequence are ½ and 8, respectively. Determine the 1st term and the formula for the nth term.