Arithmetic Sequences--the basics only Explicit Formula

An arithmetic sequence is one in which...

• a constant number is multipled

• a constant number is divided

• a constant number is added to each term

• there is not pattern

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.IF.A.3

CCSS.HSF.LE.A.2

Is this an arithmetic sequence? 1, 2, 3, 4, 5...

• Yes because you are multiplying by one every time.

• Yes because you are adding 1 each time.

• No because it starts at 1.

• No because it doesn't start at 0.

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.2

Is this an arithmetic sequence? 3, 6, 9, 13, 17, 21...

• No because there is not a common difference every time.

• No because it is not subtracting

• Yes because you are adding 3 or 4 every time

• Yes because you are adding 3 every time

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.IF.A.3

CCSS.HSF.LE.A.2

What is the common difference? 5, 7, 9, 11, 13 ...

• -1

• +1

• -2

• +2

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.IF.A.3

CCSS.HSF.LE.A.2

What is the common difference? 15, 10, 5, 0, -5, -10 ...

• +10

• -10

• -5

• +5

Tags

CCSS.HSF.BF.A.2

How do you set up the explicit formula for this sequence? 5, 7, 9, 11, 13 ...

• $a_n=\ -5+\left(n-1\right)\left(-2\right)$

• $a_n=-5+\left(n-1\right)\left(2\right)$

• $a_n=\ 5+\left(n-1\right)\left(-2\right)$

• $a_n=\ 5+\left(n-1\right)\left(2\right)$

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.2

How do you set up the explicit formula for this sequence? 15, 10, 5, 0, -5 ...

•  $a_n=\ -5+\left(n-1\right)\left(-15\right)$ 

•  $a_n=\ -5+\left(n-1\right)\left(15\right)$ 

•  $a_n=\ 15+\left(n-1\right)\left(-5\right)$ 

•  $a_n=\ 15+\left(n-1\right)\left(5\right)$ 

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.2

Simplify this explicit formula:

 $a_n=\ 5+\left(n-1\right)\left(2\right)$  

•  $a_n=2n\ +7$  

•  $a_n=2n\ -7$  

•  $a_n=2n\ +3$  

•  $a_n=2n\ +5$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.A.2

CCSS.HSF.IF.C.8

Simplify this explicit formula: $a_n​=15+(n−1)\left(-5\right)$  

•  $a_n=-5n+20$  

•  $a_n=-5n+15$  

•  $a_n=-5n+10$  

•  $a_n=5n+15$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.A.2

CCSS.HSF.IF.C.8

Write the explicit formula for this sequence:

100, 112, 124, 136 ...

•  $a_n=12n\ +100$ 

•  $a_n=-12n\ +100$ 

•  $a_n=12n+112\$ 

•  $a_n=12n\ +\ 88$ 

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.2