Arithmetic and Geometric Sequences

​

Fill in the Blanks

What is the common difference of this sequence?

Fill in the Blanks

What is the zeroth term of this sequence?

Explicit Equations

• An explicit formula tells exactly how to find any specific term in a sequence

​

​f(0)=-4

​f(n)=f(0)+dn

​f(n)= -4+5n

Multiple Choice

What is the explicit equation of this sequence?

• $$t\left(n\right)=3n-11$$

• $$t\left(n\right)=-11n+3$$

Multiple Choice

Write the EXPLICIT rule for the arithmetic sequence

-10, -3, 4, 11,...

NOTE: a_n = output (y) and n = input (x)

• a_n = 10n + 17

• a_n = 7n - 17

• a_n = -7n + 17

• a_n = 7n + 3

Multiple Choice

Given the sequence:
 25, 21, 17, 13,...
Write the explicit equation that models the sequence.  (Hint:  Simplify your equation.)

• a_n = 4n + 29
• a_n = -4n + 25
• a_n = -4n + 29
• a_n = 4n + 25

Things to know first...

​t(1)=-8
t(1+1)=t(2)=-5

Find your first term and common difference.

​Recursive Arithmetic Sequences

Recursive Formula:​
t(1)=-8
t(n)=t(n-1)+3

Find your common difference
+3

Fill in the Blanks

Find the first 3 terms of the sequence.

$t\left(1\right)=5\$  
$t\left(n\right)=t\left(n-1\right)+3$  

Fill in the Blanks

Find the first 3 terms of the sequence.

$t\left(1\right)=5\$  
$t\left(n\right)=t\left(n-1\right)-3$  

Multiple Choice

Write the recursive rule for the arithmetic sequence

82, 76, 70, 64, ...

• a₁= 82; a_n = a_n-1 - 6

• a₁= 64;

  a_n = a_n-1 - 6

• a₁= 82; a_n = a_n-1 + 6

• a₁= 64;

  a_n = a_n-1 + 6

Multiple Choice

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

• a_n=a_n-1+11
  a₁=6
• a_n=a_n-1-4
  a₁=6
• a_n=a_n-1+9
  a₁=6
• a_n=a_n-1+6
  a₁=6

Multiple Choice

Write a recursive rule for the sequence 17, 1, -15, -31 . . .

• a_n = a_n-1 + 16
  a₁=17
• a_n = a_n-1 - 17
  a₁=17
• a_n = a_n-1 - 15
  a₁=17
• a_n = a_n-1 - 16
  a₁=17

Multiple Choice

Find the first five terms.

• $$-8,-17,-26,-35,-44$$  

• $$-18,-26,-34,-42,-50$$  

• $$-18,-28,-38,-48,-58$$  

• $$-8,-18,-28,-38,-48$$