Arithmetic and Geometric Sequences

Authored by Tony Lara

Mathematics

3rd Grade

CCSS covered

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19 questions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Using the formula $a_n=a_1+d\left(n-1\right)$ , where $a_1$ represents the first term and $d$ represents the common difference, write a formula for the sequence 18, 16, 14, 12, 10, 8, ...

$a_n=18+2\left(n-1\right)$

$a_n=18-2\left(n-1\right)$

$a_n=2+18\left(n-1\right)$

$a_n=-2+18\left(n-1\right)$

Tags

CCSS.HSF.BF.A.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Arithmetic sequences form a linear equation.
Geometric sequences form an exponential equation.
Given the geometric sequence 2, 6, 18, ..., write an explicit formula.

$a_n=6\left(2\right)^{n-1}$

$a_n=2\left(6\right)^{n-1}$

$a_n=3\left(2\right)^{n-1}$

$a_n=2\left(3\right)^{n-1}$

Tags

CCSS.HSF.BF.A.2

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

What is the fifth term for the sequence below?
$a_n=5\left(2\right)^{n-1}$
Hint: Use your calculator and replace n with 5.

a₅ = 160

a₅ = 40

a₅ = 10

a₅ = 80

Tags

CCSS.HSF.BF.A.2

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Find the first four terms of the sequence given the rule:
a_n = 4(5)^n-1

20, 100, 500, 2500

5, 20, 80, 320

4, 20, 100, 500

4, 9, 14, 19

Tags

CCSS.HSF.BF.A.2

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

What is a₅ for the sequence below?
a_n = 5 ⋅ 2^(n-1)

a₅ = 160

a₅ = 40

a₅ = 10

a₅ = 80

Tags

CCSS.HSF.BF.A.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The first three terms of an a sequence are 3, 11, and 19. Which formula represents the sequence?

a_n = 8 + 3(n-1)

a_n = 8(3)^n-1

a_n = 3 + 8(n-1)

a_n = 3 + 8n

Tags

CCSS.HSF.BF.A.2

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Write a recursive formula for the following sequence:
10, 5, 0, -5,...

a₁= 10

a_n= a_n-1 - 5

a₁= 10

a_n= a_n-1 + 5

a₁= 10

a_n= a_n (5)

a₁= 10

a_n= a_n-1 (5)

Tags

CCSS.HSF.BF.A.2

10.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A sequence can be generated by using $a_n=4\ a_{\left(n-1\right)},$ where $a_1=6$ and n is a whole number greater than 1. What are the first four terms in the sequence?

6, 24, 96, 384

6, 10, 14, 18

6, 20, 100, 500

6, 20, 76, 300

Tags

CCSS.HSF.BF.A.2

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Arithmetic and Geometric Sequences

Using the formula $a_n=a_1+d\left(n-1\right)$ , where $a_1$ represents the first term and $d$ represents the common difference, write a formula for the sequence 18, 16, 14, 12, 10, 8, ...

Arithmetic sequences form a linear equation.
Geometric sequences form an exponential equation.
Given the geometric sequence 2, 6, 18, ..., write an explicit formula.

What is the fifth term for the sequence below?
$a_n=5\left(2\right)^{n-1}$
Hint: Use your calculator and replace n with 5.

Find the first four terms of the sequence given the rule:
a_n = 4(5)^n-1

What is a₅ for the sequence below?
a_n = 5 ⋅ 2^(n-1)

The first three terms of an a sequence are 3, 11, and 19. Which formula represents the sequence?

Write a recursive formula for the following sequence:
10, 5, 0, -5,...

Write the recursive formula for 6, 17, 28, 39, 50....

Given the recursive formula, find the first four terms:
a_n = a_n-1 + 5
a₁ = -16

A sequence can be generated by using $a_n=4\ a_{\left(n-1\right)},$ where $a_1=6$ and n is a whole number greater than 1. What are the first four terms in the sequence?

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Arithmetic and Geometric Sequences

Using the formula an=a1+d(n−1)a_n=a_1+d\left(n-1\right)an​=a1​+d(n−1) , where a1a_1a1​ represents the first term and ddd represents the common difference, write a formula for the sequence 18, 16, 14, 12, 10, 8, ...

Arithmetic sequences form a linear equation.Geometric sequences form an exponential equation.Given the geometric sequence 2, 6, 18, ..., write an explicit formula.

What is the fifth term for the sequence below? an=5(2)n−1a_n=5\left(2\right)^{n-1}an​=5(2)n−1 Hint: Use your calculator and replace n with 5.

Find the first four terms of the sequence given the rule:an = 4(5)n-1

What is a5 for the sequence below? an = 5 ⋅ 2(n-1)

The first three terms of an a sequence are 3, 11, and 19. Which formula represents the sequence?

Write a recursive formula for the following sequence: 10, 5, 0, -5,...

Write the recursive formula for 6, 17, 28, 39, 50....

Given the recursive formula, find the first four terms:an = an-1 + 5a1 = -16

A sequence can be generated by using an=4 a(n−1),a_n=4\ a_{\left(n-1\right)},an​=4 a(n−1)​, where a1=6a_1=6a1​=6 and n is a whole number greater than 1. What are the first four terms in the sequence?

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Using the formula $a_n=a_1+d\left(n-1\right)$ , where $a_1$ represents the first term and $d$ represents the common difference, write a formula for the sequence 18, 16, 14, 12, 10, 8, ...

Arithmetic sequences form a linear equation.
Geometric sequences form an exponential equation.
Given the geometric sequence 2, 6, 18, ..., write an explicit formula.

What is the fifth term for the sequence below?
$a_n=5\left(2\right)^{n-1}$
Hint: Use your calculator and replace n with 5.

Find the first four terms of the sequence given the rule:
a_n = 4(5)^n-1

What is a₅ for the sequence below?
a_n = 5 ⋅ 2^(n-1)

Write a recursive formula for the following sequence:
10, 5, 0, -5,...

Given the recursive formula, find the first four terms:
a_n = a_n-1 + 5
a₁ = -16

A sequence can be generated by using $a_n=4\ a_{\left(n-1\right)},$ where $a_1=6$ and n is a whole number greater than 1. What are the first four terms in the sequence?