Geometric Sequence Word Problems

Carey is organizing her books and putting them on shelves. She put 2 books on the first shelf, 8 books on the second shelf, 32 books on the third shelf, and 128 books on the fourth shelf. What kind of sequence is this?

• Geometric

• Arithmetic

• Both

• Neither

This image shows how a certain bacteria grows in a petri dish. What is the common ratio of this sequence?

• 4

• 3

• 2

• 6

Which sequence type, and common ratio/difference is correct for the table?

• arithmetic

  common ratio = 2

• geometric

  common ratio = 2

• arithmetic

  common difference = 2

• geometric

  common difference = -2

Find the first 6 terms of the sequence

• 1, 2, 6, 18, 54, 162

• 2, 6, 18, 54, 162, 486

• -2, -6, -18, -54, -162, -486

• -2, 1, 4, 7, 10, 13

On a scale of 1-5, 1 meaning "I have no clue what is going on" to 5 meaning "I got it completely," how would you rate your understanding of identifying Geometric  Sequences: Graphing & Word Problems ?

• 1

• 2

• 3

• 4

• 5

A child on a swing is let go from a vertical height so that the distance he travels in the first back - and - forth swing is exactly 9 feet.  If each swing decreases the distance by 85 % write a geometric series that expresses the distance the child travels in feet. 

• a_n = 9 (.85)^n-1

• a_n = 9 (.15) ^{n - 1}

• a_n = (.85) (9) ^n-1

Match the following for the prompt: A bacteria colony starts with 5 bacteria and triples every hour.

• Initial value

• 3

• Explicit equation

• Common ratio

• 5

• Recursive equation

Daisy received $2 on her first birthday. Each year, the amount of money she received tripled. How much money will she receive on her 5^th birthday?

• $10

• $300

• $162

• $416

You have $729 in the bank on Day 1, $243 on Day 2, and $81 on Day 3. Write the explicit formula that expresses the sequence.

• a_n = 729(1/3)^n-1

• a_n = 729(3)^n-1

• a_n = 1/3(a_n-1)

• a_n = 1/3(729)^n-1

The local power company plans to raise rates to cover the increased cost of producing power. They determine the costs will increase by 4.2% per year for the next 10 years. If you paid a total of $1031.60 for power last year, what would you expect to pay for power over the next 10 years? 
(Hint: Find a₁, a₁₀, and r)

• $13,020.97

• $10,316.00

• $2,704.97

• $12,220.97