Geometric Series Word Problems

A pendulum that is released to swing freely travels 18 cm on the first swing. On each successive swing, the pendulum travels 80% of the distance of the previous swing. What is the total distance the pendulum swings?

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

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

• 4

• 3

• 2

• 6

Answer explanation

The number DOUBLES

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

Find the sum of the first 5 terms of the sequence whose first term is 7 and the common ratio is 7.

• 19607

• 19608

• 19609

• 19610

What is the sum of the first three terms of the sequence 3, 15, 75,375...?

• 15

• 67

• 93

• 125

Build the series knowing that it has 5 terms, starts with -2 and has a common ratio of -4.

• -2 - 8 - 32 - 128 - 512

• -2 + 8 - 32 + 128 - 512

• 2 + 8 + 32 + 128 + 512

• -2 + 8 + 32 - 128 + 512

What kind of sequence is illustrated below?

400, 200, 100, 50, 25, ...

• Arithmetic, d = ½

• Geometric, r = ½

• Neither

Evaluate (find the sum) of this geometric series.

• 36352

• 52428

• 46121

• 41131

• -4/5

What is the sum of the first ten terms of the sequence 4, -12, 36, -108 . . . ?

• 59,050

• -59,048

• -78,732

• 118,096