Arithmetic Sequences

Arithmetic Sequences

​What is an event that takes place at regular intervals?

​What you think an arithmetic sequence is?

​Dave bowled 10 games. How could Dave calculate an average for the 10 games?

Today's Objectives
1. Define an arithmetic Sequence.
2. Find the nth term of an arithmetic sequence
3. Find the sum of an arithmetic series

​Please go to managebac files and find the notes folder and look for 'Summary Notes for Whole Course' (pdf). Read the notes on page 10 (Arithmetic Sequences), page 12 (sigma notation) then answer the questions on the next slides.

Multiple Choice

Find the common difference: -34, -29, -24, -19, ...

• d = -5
• d = 5
• d = -6
• d = 6

Multiple Choice

The first three terms of an arithmetic sequence are as follows

13, 19, 25

What are the next two terms of the sequence?

• 31 and 37

• 31 and 36

• 30 and 37

• 30 and 36

Multiple Choice

Which sequence is NOT an arithmetic sequence?

• 12, 18, 24, 30,...

• 10, 3, -4, -11,...

• 2, 4, 8, 16,...

• 16, 20, 24, 28,...

Multiple Choice

Define arithmetic sequences.

• A sequence whose terms change by adding the same number each time.

• A sequence whose terms change by multiplying the same number each time.

• A sequence whose terms change by dividing the same number each time.

• A list of numbers that often (but not always) form a pattern.

Multiple Choice

Find the sum of this arithmetic series:

3, 7, 11, 15, 19, 23, 27

• 210

• 105

• 30

• 15

Multiple Choice

Sometimes sequences are described in subscript notation.

Given $$a_1=-5$$  and $$a_n=a_{n-1}+3$$  , what are the first 4 terms in the sequence?

• -5, -2, 1, 4

• -5, -8, -11, -14

• 3, -2, -7, -12

• 3, -15, 75, -375

Multiple Choice

Write the explicit rule for the arithmetic sequence
12, 10, 8, 6, ...

• a_n = 12n - 14
• a_n = 2n - 14
• a_n = -2n + 14
• a_n = -12n + 14

Multiple Choice

Which kind of sequence has a common difference?

• Arithmetic
• Geometric

Match

Match the following

• $$a_1$$

• n

• What is being added in an arithmetic sequenc

• Sn

First Term

term number

Common Difference (d)

Sum of an arithmetic series

• First Term

• term number

• Common Difference (d)

• Sum of an arithmetic series

Multiple Choice

Which of the following will give the sum of the first 6 term of the following series:

1 + 7 + 13 + 19 + ...

• $$\frac{6}{2}\left(1+31\right)$$

• $$\frac{1}{2}\left(6+2\right)$$

• $$1\left(\frac{1-\left(6\right)^6}{1-6}\right)$$

• $$6\left(\frac{1-\left(1\right)^6\ }{1-1}\right)$$

Poll

Rate your current understanding of today's lesson

• 1 = I am lost

• 2 = I am starting to get it but need practice

• 3 = I've got this

• 4 = I can teach it

​Stop Here for now

​Go to the Kognity Assignment  'Arithmetic Sequences and Series Practice' or find a copy of it on managebac in the folder Practice Problems.

 

https://app.kognity.com

We can do these questions in your groups or as a class. Please write your answers down in your notebook.

Poll

Rate your current understanding of today's lesson

• 1 = I am lost

• 2 = I am starting to get it but need practice

• 3 = I've got this

• 4 = I can teach it

Open Ended

Exit Ticket A: Define common difference as it relates to an arithmetic sequence.

Open Ended

Exit Ticket B: An arithmetic sequence begins: 5, 11, 17, 23

a) Find the value of the 15^th term.

b) Find the sum of the first 15 terms.

Open Ended

Exit Ticket C:

Explain what each term in the formula for the sum of an arithmetic series represents (name the variables).

Open Ended

Exit Ticket D:

If you are given the sum of an arithmetic series, the value of the first term, and the number of terms

explain how you could:

a) Find the value of the last term

b) Find the common difference

Poll

Rate your current understanding of today's lesson

• 1 = I am lost

• 2 = I am starting to get it but need practice

• 3 = I've got this

• 4 = I can teach it