Geometric Sequences

Vocabulary 1

100

a₁

The first term in a sequence

200

3, 9, 27, 81 … The “…” means

3, 9, 27, 81 … The “…” means

300

-2, 4, -8, 16, -32 … -32 is the ____ term in the sequence.

5^th

400

In order to solve for a term, you must know the value of its preceding term.

recursive formula

500

In the explicit formula, 𝑎_n = 𝑎₁(𝑟)^n-1 , what does 𝑟 represent?

common ratio

Vocabulary 2

100

a_n

Any term in a sequence

200

84, 42, 21, 10.5, 5,25… are the actual _____ of the sequence.

terms

300

What is a geometric sequence?

Each term in a sequence is multiplied by a common number repeatedly

400

To solve for a term, you need to know the first term of the sequence and the difference.

Explicit Formula

500

Which formula is 𝑎_n = 𝑎_n-1(𝑟)?  

Recursive Formula 

What is the term?

100

Find the 9^th term in the sequence: 3, 6, 12, 24, 48 …

768

200

Find the 7^th term in the sequence: 243, 81, 27, 9…

1/3

300

What are the next three terms of the sequence 140, 70, 35, 17 1 2 …

8 3/4, 4 3/8, 2 3/16

400

What are the next three terms in the sequence 3, -9, 27, -81…

243, -729, 972

500

Use the explicit formula to find the 12^th term of the sequence 2, -6, 18, -54, 162 …

1,062,882

Application

100

Sam plans to double his savings each day. He starts with $0.03 in his account. How much will be saved after 30 days?

$16,106,127.36

200

The number of bacteria on a piece of toast triples every hour. If there is only one bacteria cell now, how many will there be in 24 hours?

94,143,178,827

300

Today Ashley is training for a marathon by running 10 minutes. She plans to double her training time each day. How many minutes will she run on day 7?

640

400

You are golfing with a buddy and you bet one $1 for hole #1 and double your wager for each hole thereafter. How much can you win on the 18th hole?

$131,072

500

You find a job that pays you $12 an hour and promises to pay you 5% more every year. What is your hourly wage after 30 years Round your answer to the nearest cent?  

$49.39

Random

100

What is the common ratio of the sequence? 𝑎_n = −2(−3)^n-1

-3

200

Write the recursive formula for -4, -24, -144, -864 …

a_n= 6(a_n-1)

300

Use the explicit formula to find the 21^st term of the sequence 9, -18, 36, -72 …

9,437,184

400

Find the first three terms in the sequence 𝑎_n = −2.5(4)^n-1

-2.5, -10, -40

500

In a certain region, the number of highway accidents increase by 20% over a four year period. How many accidents were there in 2006 if there were 5,100 accidents in 1998?

7,344