Geometric Series Word Problems Quiz

Authored by Anthony Clark

Mathematics

10th Grade

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FILL IN THE BLANKS QUESTION

1 min • 1 pt

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?

(a)

Answer explanation

Infinite SUM
$S=\frac{a_1}{1-r}$
$S=\frac{18}{1-0.8}=90$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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

Answer explanation

Term Value
$a_n=a_1\ \left(r\right)^{\left(n-1\right)}$
$a_5=2\left(3\right)^{\left(5-1\right)}=162$

Tags

CCSS.HSF.BF.A.2

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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

Answer explanation

The number DOUBLES

Tags

CCSS.HSF.BF.A.2

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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

Answer explanation

$a_n=a_1\left(r\right)^{\left(n-1\right)}$
$a_n=729\ \left(\frac{1}{3}\right)^{\left(n-1\right)}$

Tags

CCSS.HSF.BF.A.2

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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

Answer explanation

FINITE SUM
$S_n=a_1\left(\frac{1-r^n}{1-r}\right)$
$S_5=7\left(\frac{1-7^5}{1-7}\right)=19607$

Tags

CCSS.HSA.SSE.B.4

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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

125

Tags

CCSS.HSA.SSE.B.4

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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

Tags

CCSS.HSF.BF.A.2

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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?

(a)

Infinite SUM
$S=\frac{a_1}{1-r}$
$S=\frac{18}{1-0.8}=90$

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?

Term Value
$a_n=a_1\ \left(r\right)^{\left(n-1\right)}$
$a_5=2\left(3\right)^{\left(5-1\right)}=162$

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

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.

$a_n=a_1\left(r\right)^{\left(n-1\right)}$
$a_n=729\ \left(\frac{1}{3}\right)^{\left(n-1\right)}$

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

FINITE SUM
$S_n=a_1\left(\frac{1-r^n}{1-r}\right)$
$S_5=7\left(\frac{1-7^5}{1-7}\right)=19607$

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

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

What kind of sequence is illustrated below?
400, 200, 100, 50, 25, ...

Evaluate (find the sum) of this geometric series.

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

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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? (a)

Infinite SUM S=a11−rS=\frac{a_1}{1-r}S=1−ra1​​ S=181−0.8=90S=\frac{18}{1-0.8}=90S=1−0.818​=90

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

Term Value an=a1 (r)(n−1)a_n=a_1\ \left(r\right)^{\left(n-1\right)}an​=a1​ (r)(n−1) a5=2(3)(5−1)=162a_5=2\left(3\right)^{\left(5-1\right)}=162a5​=2(3)(5−1)=162

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

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.

an=a1(r)(n−1)a_n=a_1\left(r\right)^{\left(n-1\right)}an​=a1​(r)(n−1) an=729 (13)(n−1)a_n=729\ \left(\frac{1}{3}\right)^{\left(n-1\right)}an​=729 (31​)(n−1)

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

FINITE SUM Sn=a1(1−rn1−r)S_n=a_1\left(\frac{1-r^n}{1-r}\right)Sn​=a1​(1−r1−rn​) S5=7(1−751−7)=19607S_5=7\left(\frac{1-7^5}{1-7}\right)=19607S5​=7(1−71−75​)=19607

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

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

What kind of sequence is illustrated below?400, 200, 100, 50, 25, ...

Evaluate (find the sum) of this geometric series.

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

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

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?

(a)

Infinite SUM
$S=\frac{a_1}{1-r}$
$S=\frac{18}{1-0.8}=90$

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?

Term Value
$a_n=a_1\ \left(r\right)^{\left(n-1\right)}$
$a_5=2\left(3\right)^{\left(5-1\right)}=162$

$a_n=a_1\left(r\right)^{\left(n-1\right)}$
$a_n=729\ \left(\frac{1}{3}\right)^{\left(n-1\right)}$

FINITE SUM
$S_n=a_1\left(\frac{1-r^n}{1-r}\right)$
$S_5=7\left(\frac{1-7^5}{1-7}\right)=19607$

What kind of sequence is illustrated below?
400, 200, 100, 50, 25, ...