Sequences Review

Arithmetic Recursive

100

What is the Arithmetic Recursive equation?

a_n = a_n-1 + d

200

2, 4, 6, 8, 

Use a Arithmetic Recursive equation to find the 5th term in the sequence. 

a₅ = a_5-1 + d

10 = 8 + 2

300

-10, -7, -4, -1, 2

Use a Arithmetic Recursive equation to find the 6th term of the Sequence. 

a₆ = a_6-1 + d

5 = 2 + 3 

400

90, 78, 66, 54, 42 

Use a Arithmetic Recursive equation to find the 6th term in the sequence.

a₆ = a_6-1 + (-d)

30 = 42 + (-12)

500

Owen runs 6 miles on day one, then 11 miles on day two, then 16 miles on day three. Following the pattern, how many miles will he run on day 4. 

a₄ = a_4-1 + d

21 = 16 + 5

Arithmetic Explicit

100

What is the Arithmetic Explicit equation?

a_n = a₁ + d(n-1)

200

3, 6, 9, 12, 15

Use a Arithmetic Explicit equation to find the 10th term of the sequence. 

a₁₀ = a₁ + d(10-1)

30 = 3 + 3(9)

300

8, 13, 18, 23, 

Use a Arithmetic Explicit equation to find the 16th term of the sequence. 

a₁₆ = a₁ + d(16-1)

83 = 8 + 5(15)

400

30, 10, -10, -30 

Use a Arithmetic Explicit equation to find the 40th term in the sequence. 

a₄₀ = a₁ + d(40-1)

-750 = 30 + (-20 * 39)

500

Parker is working at Taco Bell, he makes 5 dollars a day. On day one he has 10 dollars in his bank account. How much money will Parker have in 50 days? 

a₅₀ = a₁ + d(50-1)

255 = 10 + 5(49)

Geometric Recursive

100

What is the Geometric Recursive equation?

a_n = a_{n-1 *} r

200

4, 8, 16, 32

Use a Geometric Recursive equation to find the 5th term of the sequence. 

a₅= a_{5-1 *} r

64 = 32 _* 2

300

3, 9, __, 81

Use a Geometric Recursive equation to find the 3rd term of the sequence. 

a₃ = a_3-1 * r

27 = 9 _* 3

400

-2, 4, -8, 16, -32

Use a Geometric Recursive equation to find the 6th term in the sequence. 

a₆ = a_{6-1 *} (-r)

64 = -32 _* (-2)

500

Liv is in a rocket ship going to the moon. Every minute her speed increases, 300mph, 600mph, 1200mph. How fast will she be going 4 min after her ship takes off?

a₄ = a_4-1 * (r)

2400 = 1200 _* 2

Geometric Explicit

100

What is the Geometric Explicit equation? 

a_n = a_{1 *} r^(n-1)

200

6, 12, 24, 48

Use a Geometric Explicit equation to find the 7th term in the sequence. 

a₇ = a_{1 *} r^7-1

384 = 6 * 2⁶

300

10, 30, 90, 270

Use a Geometric Explicit equation to find the 10th term in the sequence. 

a₁₀ = a_1 * r^10-1

196,830 = 10 _* 3⁹

400

8000, 4000, 2000, 1000, 500

Use a Geometric Explicit equation to find the 7th term of the sequence

a₇ = a_{1 *} r^7-1

125 = 8000 _* (½)⁶

500

Mr. Gregory was born with 100 aura points. Every year he is alive his amount of aura triples! Write an equation to find the amount of aura Mr. Gregory will have when he is 50 years old. 

a₅₀ = 100 _* 3⁴⁹

What's that pattern?

100

7, 12, 17, 22, 27, ___

1) Find the Next term in the sequence

2) What is the pattern (d/r)

1) 32

2) Add by 5 (d=5)

200

-4 , 12 , 36, 108, 324 , ___

1) What is the next term in the sequence

2) What is the pattern   (d/r)=___

1) 972

2) multiply by 3

300

SPEED QUESTION: FIRST GROUP TO RAISE THEIR HANDS

Write the pattern down! 

: 2, 4, 4, 4, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 

1-2, 3-4's  , 5-6's , 7-8's 

or 1,2,3,4,5,6,7,8.

400

4, 12, 36, 108, ___

What is the common ratio?

Arithmetic or geometric?

Next term?

ratio (r) = 3

Geometric

Next term = 324

500

1, 1, 2, 3, 5, 8, 13

Name the next term 

Name the man who this sequence is named after. (Italian and famous last name starts with F)

21

&

Leonardo FIBONACCI