Arithmetic Sequence: The Adventure

Arithmetic Sequence : The Adventure

Multiple Choice

What is an Arithmetic Sequence?

• A sequence where each term is determined by multiplying a constant value to the previous term.

• A sequence where each term is determined by adding a constant value to the previous term.

• A sequence where each term is a random number.

• A sequence where each term is equal to the first term.

Arithmetic Sequence

An arithmetic sequence is an ordered set of numbers that have a common difference between each consecutive term. There is common difference in this sequence.

Multiple Choice

What is common difference?

• The total sum of all terms in the sequence.

• The value that is multiplied by each term to get the next term.

• The consistent value added (or subtracted) to each term to get to the next term.

• The largest term in the sequence.

​Common difference

If the difference between every pair of consecutive terms in a sequence is the same, this is called the common difference. For example, the sequence 4,7,10,13,... has a common difference of 3. A sequence with a common difference is an arithmetic progression.

Multiple Choice

How to calculate the common difference?

• d = a * (n + 1) / a_n

• d = a_n - a / (n - 1)

• d = a - (n - 1) * a_n

• d = a_n - a_n-1

d = 5 - 2
= 3
Therefore the common difference is 3.

​Solution:

Ex. "In the sequence 2, 5, 8, 11, ...
Given:
a₂ = 5
a₁ = 2

​d = a_n - a_n-1

​To calculate common difference

d = 40 - 30
= 10
Therefore the common difference is 10.

​Solution:

Ex. "In the sequence 10, 20, 30, 40
Given:
a₄ = 40
a₃ = 30

​d = a_n - a_n-1

​To calculate common difference

Multiple Choice

Find the common difference of this sequence: 34, 50, 66, 78, ...

• 26

• 16

• 36

• 0.6

Finding the n^th term

​Formula: a_n= a + (n - 1) d

Where:

a_n = n^th term of the arithmetic sequence.
a = the first term of the arithmetic sequence.
n = is the position of the term you want to find.
d = Common difference

 a₅ = a₁ + (5 - 1) 3
= -6 + 4 * 3
= -6 + 12
= 6

The 5th term in this sequence is 6.

Solution:

Given:
 a₁ = -6

d = 3
Find the a₅

Example: -6, -3, 0, 3, __

Finding the next term

Multiple Choice

Try this: Find the 8th term in the previous sequence -6, -3, 0, 3, 6, ...

• 10

• 25

• 35

• 15

 a₈ = -6 + (8 - 1) 3
= -6 + 7 * 3
= -6 + 21
= 15

The 8th term in this sequence is 15.

Solution:

a₁ = -6

d = 3

Given:

Find the 8th term in the previous sequence -6, -3, 0, 3, 6, ...

Multiple Choice

Determine if the sequence is arithmetic. If yes, identify the common difference.

A) 7, 10, 13, 16, ...

• Yes

• No

• Maybe

Multiple Choice

Determine if the sequence is arithmetic. If yes, identify the common difference.

B) 14, 8, 2, − 4, ...

• Yes

• No

• Maybe

Multiple Choice

Determine if the sequence is arithmetic. If yes, identify the common difference.

C) 1, 4, 9, 16, ...

• Yes

• No

• Maybe