Review on Different Types of Sequences

Review on Different Types of Sequence

• ​Always turn your camera on.

• Proper use of chat box.

• Participate and have fun.

​Reminders:

• ​Categorize sequences based on their characteristics, such as number sequence, arithmetic, geometric, or fibonacci.

• Analyze sequences to identify patterns or regularities in the terms.

• Learn how to find the common difference in an arithmetic sequence and common ratio in geometric sequence.

• Calculate specific terms of an arithmetic and geometric sequence.

• Find the nth term formula for arithmetic and geometric sequences.

​Objectives:

​  "Why should I study sequences and series?"

Enduring understanding

Multiple Choice

Who develop the Fibonacci Sequence?

• Rene Descartes

• Euclid

• Leonardo of Pisa

Multiple Choice

What do you call with a constant number that is being added or subtracted to each tern in a sequence?

• Constant

• Common Ratio

• Common Difference

Multiple Choice

In an arithmetic sequence defined as a_n = a₁ + (n – 1)d, what do you call d ?

• first term

• nth term

• common difference

• distance

Multiple Choice

It is a sequence where each term after the first is obtained by multiplying the preceding term by the same constant.

• Arithmetic

• Geometric

• Harmonic

• Fibonacci

Multiple Choice

What do you call a sequence in which each term after the first is obtained by adding a constant d to the preceding term?

• Arithmetic

• Geometric

• Harmonic

• Fibonacci

Multiple Choice

What is the next term in geometric sequence 5,10,20,__?

• 50

• 40

• 30

• 25

Multiple Choice

What is the next term of the sequence 1,4,9,16,...?

• 21

• 25

• 30

• 31

Multiple Choice

Determine the 5^th term of the sequence given the nth term a_n = 3n – 4.

• -4

• 3

• 11

• 15

Multiple Choice

Find first three terms of this sequence:

term = position number 2x + 10

• 21, 23, 25

• 12, 13, 14

• 12, 14, 16

• 22, 24, 26

Multiple Choice

Noora makes a sequence of numbers , starting with 13. She subtracted 4 each time. What are the next 3 numbers in the sequence?

• 14, 17, 20

• 8, 4, 0

• 9, 5, 1

Multiple Choice

Which of the following numbers is the 8th term of sequence 

$$a_{n_{ }}=\frac{2n}{4}$$  ?

• 4          

• 8

• 12

• 16

Multiple Choice

What are the first three terms of the sequence with the nth term a_n = n² + 2?

• 3, 6, 15

• 3, 6, 10

• 3, 6, 8

• 3, 6, 11

Multiple Choice

Is this sequence arithmetic, geometric, fibonacci, or neither?
{26, 22, 18, 14, ...}

• Arithmetic
• Geometric
• Neither

Multiple Choice

Is this sequence Arithmetic, Geometric, fibonacci or Neither?
{14, 22, 30, 38, .. }

• Arithmetic
• Geometric
• Neither

Multiple Choice

Is this sequence Arithmetic, Geometric, Fibonacci or Neither?
{2, 9, 7, 14, 12, 19, ... }

• Arithmetic
• Geometric
• Neither

Multiple Choice

What is the common ratio of this sequence?
{2, 10, 50, 250, ... }

• 1,250
• 5
• 10
• 50

Multiple Choice

Create the explicit formula for the sequence:
2, 8, 14, ...
(Hint:  Write your formula and then simplify it.)

• a_n=2+6n
• a_n=-6+6n
• a_n=6n-4
• a_n=4-6n

Multiple Choice

Find the first term of the given sequence:
a₁₄=68
d=3

• 14
• 20
• 26
• 29

Multiple Choice

Find the 25th term of the sequence if a₁ = 5 and d = 0.5

• 18
• 17
• 15
• 14

Multiple Choice

In the geometric sequence

2, 6, 18, n, 162, ..., what is the value of n?

• 54

• 90

• 24

• 36

Multiple Choice

What is the 5th term of the sequence 7, 14, 28, ...?

• 72

• 48

• 56

• 112

Multiple Choice

Solving for the nth term of geometric sequence, given that a₁ = 1 and r= 2, what is the value of the 4th term?

• 2

• 8

• 4

• 16

Multiple Choice

What is the 5th term of the geometric sequence -2, -8, -32, -128, ...?

• -2048

• -512

• -256

• -384

Multiple Choice

What is a₅ in the sequence defined as follows?
a_n = 5 ⋅ 2^(n-1) 

• a₅ = 160
• a₅ = 40
• a₅ = 10
• a₅ = 80

Fill in the Blanks

Draw

Draw your experiences today during math class.