M3 L1-2 Review

M3 L1-2 Review

Sequence Review Day!!

Multiple Choice

Today's bellwork question, Do the 2 equations represent the same sequence?

 $a_n=a_{\left(n-1\right)}+4$  

 $a_n=4n+5$  

• YES

• NO

Consider the sequence following a minus 8 pattern: 9, 1, -7, -15,...

• a.) Write an explicit formula for the sequence.

• b.) Write a recursive formula for the sequence.

• c.) Find the 38th term of the sequence.

Poll

1a.) Write an explicit formula for the sequence 9, 1, -7, -15,...

• $f\left(n\right)=9-8\left(n-1\right)$

• $f\left(n\right)=f\left(n-1\right)-8$

• $f\left(n\right)=-8n+17$

• $a_n=a_{\left(n-1\right)}-8$

Poll

1b.) Write a recursive formula for the sequence 9, 1, -7, -15,...

• $a_n=a_{\left(n-1\right)}-8$

• $f\left(n\right)=f\left(n-1\right)-8$

• $f\left(n+1\right)=f\left(n\right)-8$

Poll

1c.) Find the 38th term for the sequence 9, 1, -7, -15,...

• 38

• -287

• 9

Lesson 1 Homework Questions?

Please open your notebooks to week 13: L1 Problems

Multiple Choice

What is the 15th term of the sequence an = -3n+50

• 95
• -5
• 5
• -95

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

Multiple Choice

Find the 32nd term of this sequence.
34, 37, 40, 43, ...

• 32
• 64
• 127
• 356

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 22nd term of the following sequence:
5, 8, 11, ...

• 14
• 68
• 63
• 71

Multiple Choice

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

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

Multiple Choice

Write the recursive formula of 13, 9, 5...

• a_n=a_n-1-4
• a_n=a_n-1+3
• a_n=a_n-1-5
• a_n=a_n-1+4

Multiple Choice

The recursive formula is used to find the next value in a sequence of numbers.

• True
• False

Multiple Choice

The explicit formula is used to find a specific term in a sequence.

• True
• False

Multiple Choice

What is the explicit rule for the sequence:
11, 22, 44, 88...

• a_n = 2(11)^n-1
• a_n = 11x2
• a_n = 11(2)^n-1
• a_n+1 = a_{n *} 2;  a₁ = 11

Multiple Choice

Find the first four terms of the sequence.

a_n= 3(4)ⁿ

• 12, 48, 192, 768

• 12, 144, 1728, 20736

• 12, 24, 36, 48

• 3, 12, 48, 192

Multiple Choice

Which sequence has a pattern of "multiply by 4?"

• 2, 4, 8, 16,...

• 4, 12, 36, 108,...

• 1, 4, 7, 10,...

• 3, 12, 48, 192,...

Multiple Choice

A sequence is _______.

• a set of numbers in a specific order.

• a formula used to find a number.

• the term after a_n.

• a collection of data.

Multiple Choice

Given the sequence 4, 11, 18, 25...... what is a₃ ?

• 4

• 11

• 18

• 25

Multiple Choice

The 6th term of the sequence 4,7,10,13 are

• 19

• 15

• 18

• 16

Multiple Choice

What is the next term in the sequence 12, 31, 40, 49, ... ?

• 56

• 57

• 58

• 59

Multiple Choice

Write the explicit formula for the sequence.

216, 72, 24, 8, ...

• $a_n=216\cdot\left(\frac{1}{3}\right)^{\left(n-1\right)}$

• $a_n=8\cdot3^{\left(n-1\right)}$

• $a_n=216-144\left(n-1\right)$

• $a_n=216\cdot3^{\left(n-1\right)}$

Multiple Choice

Write the explicit formula for the sequence.

9, 5, 1, -3, ...

• $a_n=9+5\left(n-1\right)$

• $a_n=9-4\left(n-1\right)$

• $a_n=4+9\left(n-1\right)$

• $a_n=9\cdot4^{\left(n-1\right)}$

Multiple Choice

Given the recursive formula below, write the linear equation.
a₁ = 9
a_n = a_n-1 + 2

• y = 9 + 2n
• y = 7 + 2n 

Multiple Choice

Given the recursive formula below, find the explicit formula.  
a₀ = 1
a_n = a_n-1 + 5

• a_n = 6 + 5n
• a_n = 1 + 5n

Multiple Choice

Given the recursive formula below, find the first five terms.  
u₁ = 3
u_n = u_n-1 + 2
where n ≥ 2

• 3, 5, 7, 9, 11
• 5, 7, 9, 11, 13

Multiple Choice

Find the next three terms:
5, 8, 11, 14...

• 16, 19, 22
• 17, 19, 21
• 17, 20, 23
• 16, 18, 20