Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

In a geometric sequence, the first term,
a_(1), is equal to 4 , and the third term,
a_(3), is equal to 144 . Which number represents the common ratio of the geometric sequence?

r=5

r=6

r=7

r=8

In a geometric sequence, the first term, $a_{1}$ , is equal to $4$ , and the third term, $a_{3}$ , is equal to $144$ . Which number represents the common ratio of the geometric sequence? $\newline$ $r=5$ $\newline$ $r=6$ $\newline$ $r=7$ $\newline$ $r=8$

View step-by-step help

View step-by-step help

Scale drawings: word problems

Full solution

Q. In a geometric sequence, the first term,

a_{1}

, is equal to

4

, and the third term,

a_{3}

, is equal to

144

. Which number represents the common ratio of the geometric sequence?

\newline

r=5

\newline

r=6

\newline

r=7

\newline

r=8

Identify Given Terms: Identify the given terms in the geometric sequence. We are given the first term $a_{1} = 4$ and the third term $a_{3} = 144$ . We need to find the common ratio $r$ .
Write Formula for nth Term: Write the formula for the nth term of a geometric sequence. $\newline$ The nth term of a geometric sequence is given by $a_n = a_1 \cdot r^{(n-1)}$ , where $a_1$ is the first term and $r$ is the common ratio.
Apply Formula to Given Terms: Apply the formula to the given terms. $\newline$ We know that $a_{3} = a_{1} \cdot r^{3-1} = a_{1} \cdot r^2$ . We can substitute the given values to find $r$ . $\newline$ $144 = 4 \cdot r^2$
Solve for Common Ratio: Solve for the common ratio $r$ . Divide both sides of the equation by $4$ to isolate $r^2$ . $144 / 4 = r^2$ $36 = r^2$
Take Square Root: Take the square root of both sides to solve for $r$ . $r = \sqrt{36}$ $r = 6$

More problems from Scale drawings: word problems

Question

\newline

1,000

\text{ milligrams}

\_\_\_\_

\text{ grams}

Posted 2 months ago

Question

3

-gallon bottle of bleach costs

\$11.52

. What is the price per quart?

\newline

Posted 2 months ago

Question

Maureen can't wait to make chocolate chip zucchini bread with zucchini from her garden. Her recipe calls for

8

ounces of chocolate chips per loaf. If she has enough zucchini to make

4

loaves of zucchini bread, how many pounds of chocolate chips does she need?

\newline

Hint: There are

16

1

\newline

Write your answer as a whole number, decimal, or simplified fraction. Do not round.

\newline

Posted 2 months ago

Question

A whale is swimming due north at a speed of

30

miles per hour. Just

5

miles away, a whale-watching tour boat is traveling south, directly toward the whale, at a speed of

46

miles per hour. How long will it be before they meet? If necessary, round your answer to the nearest minute.

\_\_\_\_

\_\_\_\_

Posted 2 months ago

Question

\newline

500

=

Posted 3 months ago

Question

\newline

2,000

=

Posted 3 months ago

Question

\newline

750

=

Posted 3 months ago

Question

\newline

1,500

=

Posted 3 months ago

Question

\newline

1,500

=

Posted 3 months ago

Question

The formula for the time it takes to travel a distance of

d

at an average speed

v

\frac{d}{v}

100

-meter dash at a speed of about

7.5

meters per second. What calculation will give us the estimated duration of Tessa's dash in seconds? Choose

1

\newline

\frac{7.5}{100}

\newline

\frac{100}{7.5}

\newline

\frac{7.5}{100 \times 60}

\newline

\frac{100 \times 60}{7.5}

Posted 4 months ago