Understanding the Arithmetic Sequence Function

Understanding the Arithmetic Sequence Function

 $a_n=a_1+d\left(n-1\right)$  

Review what each of the 4 variables represent.

 $a_n$  = The term you are looking for.
 $a_1$ = 1st term 
 $d$  = Common Difference 
           (the +/- change)
 $n$  = Which number in the order are you looking for?

Example: 

10, 8, 6 , 4, _

How to use the function.
 $a_1$ = 10
 $d$  =  $a_2-a_1$  = 8 - 10 = -2
 $n$  = 5 (The blank is the 5th #)

 $a_n=a_1+d\left(n-1\right)$ 
 $a_5=10+\left(-2\right)\left(5-1\right)$  $a_5=10+\left(-2\right)\left(4\right)$  $a_5=10+\left(-8\right)=2$  

Steps:

1) Count which term are looking for.  Set as n =
2) Find the first term  $a_1$  
3) Find common difference using  $d=a_2-a_1$  
4) Plug in  $n$  ,  $a_1$  and  $d$  

 $a_n=a_1+d\left(n-1\right)$ 
5) Solve for  $a_n$  

Multiple Choice

Lesson practice Example #1
Use  $a_n=5+2\left(n-1\right)$  

Find the 3rd term.

• 2

• 5

• 7

• 9

• 11

Multiple Choice

Lesson practice Example #2
Use  $a_n=20-3\left(n-1\right)$  

Find the 5th term.

• 6

• 7

• 8

• 9

• 10

Multiple Choice

Lesson practice Example #3
Given $d=-5,\ a_1=2$ 
Find  $a_{11}$  

• 52

• 48

• -30

• -48

• -52

Lesson practice Example #3

Given  $d\ =5,\ a_1=2$  
Find   $a_{11}$  

Means... Start at 2, add by 5. Till you get to the 11th number

2, 7, 12, 17, 22​, 27, 32, 37, 42, 47, 52

          or 
 $a_{11}=a_1+d\left(11-1\right)$  

 $a_{11}=2-5\left(11-1\right)\ =\ 2-5\left(10\right)\ =\ 2-50=-48$  

Multiple Choice

Find $a_6$  .

 $a_n=10+2\left(n-1\right)$  

• 10

• 12

• 16

• 20

• 22

Multiple Choice

Find $a_4$  .

 $a_n=-4-2\left(n-1\right)$  

• 10

• 2

• -10

• -12

• -18

Multiple Choice

Find $a_{21}$  .

 $a_n=100-4\left(n-1\right)$  

• 1920

• 184

• 180

• 20

• 16

Multiple Choice

Find $a_9$  .

Which equation gives an answer of  -140.

•  $a_n=20-10\left(n-1\right)$  

•  $a_n=20+10\left(n-1\right)$  

•  $a_n=10-20\left(n-1\right)$  

•  $a_n=10+20\left(n-1\right)$ 

Multiple Choice

Find the 13th term.

 $a_n=13-3\left(n-1\right)$  

• 120

• 49

• -13

• -20

• -23

Multiple Choice

Find the 8th term.

 $a_n=-12+5\left(n-1\right)$  

• 49

• 28

• 23

• -23

• -49

Practicing Making the Equation

•  $a_n=a_1+d\left(n-1\right)$  

•  $a_1$  = 1st Term; Starting Value

•  $d$  = Common Difference =  $a_2-a_1$  

•  $n$   = # of the missing term

Multiple Choice

Remember Example #3?
Given $d=-5,\ a_1=2$ 
Find  $a_{11}$  

• 52

• 48

• -30

• -48

• -52

Multiple Choice

Given $d=10,\ a_1=24$ 
Find  $a_7$  

• 24

• 34

• 54

• 74

• 84

Multiple Choice

Given $d=-4,\ a_1=40$ 
Find  $a_{10}$  

• 0

• 4

• 36

• 40

• 80

Multiple Choice

Given $d=6,\ a_1=-35$ 
Find  $a_8$  

• 13

• 7

• 0

• -7

• -13

Multiple Choice

Given $d=12,\ a_1=2$ 
Find the 9th term

• -94

• 62

• 74

• 86

• 98