Reteach - sequences and series

Sequences and Series - Reteach

This presentation will take you through the major issues from the test. (most missed questions)

Each slide will have questions to review different information. Please have your notes packet ready to reference anything you forgot. Make sure you read the slides with information before each problem set.

Types of Sequences

Arithmetic -adding pattern with a common difference between any two consecutive terms.

Geometric - multiplying pattern with a common ratio between any two consecutive terms.

Multiple Choice

Which of the following is arithmetic?

• 1,5, 25...

• 8, 4, 2...

• 1/2, 3/4, 1...

• -3, 6, 18...

Multiple Select

Which of the following are geometric?

• 1,5, 25...

• 8, 4, 2...

• 1/2, 3/4, 1...

• -3, 6, 18...

Multiple Choice

How do we find the common ratio?

• Subtract a1 from a2. (a2 - a1)

• Subtract a2 from a1. (a1 - a2)

• divide a2 by a1

• divide a1 by a2

Multiple Choice

How do we find the common difference?

• Subtract a1 from a2. (a2 - a1)

• Subtract a2 from a1. (a1 - a2)

• divide a2 by a1

• divide a1 by a2

Writing a rule for arithmetic:

Be sure to use the correct formula, then distribute, then combine like terms. (see the worked example for more info)

Multiple Choice

Write the EXPLICIT rule for the arithmetic sequence

-10, -3, 4, 11,...

• a_n = 10n + 17

• a_n = 7n - 17

• a_n = -7n + 17

• a_n = 7n + 3

Writing a rule for geometric:

Use your formula to fill in the first term and common ratio. Always make sure your common ratio is in ( ) and never simplify the two together.

Multiple Choice

Write the explicit rule for the geometric sequence:
2, -12, 72, ...

• a_n = 72(-6)^n-1

• a_n = 2(-6)^n-1

• a_n = 2(6)^n-1

• a_n = 72(-6)^n-1

Sums to infinity:

Only works for Geometric ones whose ratio is less than one. Use your formula S_∾

Multiple Choice

If possible, find the sum of the series.

12 + 8 + 16/3 + ...

• 36

• 4

• 24

• No Sum (Diverges)

Multiple Choice

Given the rule:  a_n = 7(½)^n-1
Identify the first term.

• a_n

• 7

• ½

• n

Multiple Choice

Given the rule:  a_n = 7(½)^n-1
Identify the common ratio.

• a_n

• 7

• ½

• n-1

Multiple Choice

If possible, find the sum of the series. $$\sum_{n=1}^{\infty}8\left(\frac{1}{5}\right)^{n-1}$$  

• 8

• 8/5

• 10

• No Sum (Diverges)

The term you are going to is the n you need to plug in. Use your formula S_n. It is quick and easy but be sure your ratio is in ( ).

Geometric

The term you are going to is the n you need to plug in. Use your formula S_n. You will also have to use your a_n formula to find the last term to plug in.

Arithmetic

Sums to a specific term:

Arithmetic Example

Geometric Example

Multiple Choice

What is the sum of the series?
^{24, 28, 32, 36, ...
n = 20}

• 1240

• 100

• 1360

• 1160

Multiple Choice

What is the sum of the first ten terms of the geometric sequence 4, -12, 36, -108 . . . ?

• 59,050

• -59,048

• -78,732

• 118,096

You are now going to work to correct your test:

Be sure to read the board for directions. You may work with a partner.