Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the sum of the first 10 terms of the following series, to the nearest integer.

6,36,216,dots
Answer:

Find the sum of the first $10$ terms of the following series, to the nearest integer. $\newline$ $6,36,216, \ldots$ $\newline$ Answer:

View step-by-step help

View step-by-step help

Area and perimeter: word problems

Full solution

Q. Find the sum of the first

10

terms of the following series, to the nearest integer.

\newline

6,36,216, \ldots

\newline

Answer:

Recognize Pattern: Recognize the pattern in the series. $\newline$ The series $6$ , $36$ , $216$ , ... appears to be a geometric series where each term is multiplied by $6$ to get the next term. This means the common ratio ( $r$ ) is $6$ .
Identify Formula: Identify the formula for the sum of the first $n$ terms of a geometric series. $\newline$ The formula for the sum of the first $n$ terms of a geometric series is $S_n = \frac{a(1 - r^n)}{(1 - r)}$ , where $S_n$ is the sum of the first $n$ terms, $a$ is the first term, $r$ is the common ratio, and $n$ is the number of terms.
Plug in Values: Plug in the values into the formula. $\newline$ Here, $a = 6$ , $r = 6$ , and $n = 10$ . So, we have $S_{10} = 6(1 - 6^{10}) / (1 - 6)$ .
Calculate Sum: Calculate the sum using the formula. $\newline$ $S_{10} = 6(1 - 6^{10}) / (1 - 6)$ $\newline$ $S_{10} = 6(1 - 60466176) / (-5)$ $\newline$ $S_{10} = 6(-60466175) / (-5)$ $\newline$ $S_{10} = -362797050 / (-5)$ $\newline$ $S_{10} = 72559410$
Round to Integer: Round the sum to the nearest integer. $\newline$ The sum to the nearest integer is $72559410$ , which is already an integer, so no rounding is necessary.

More problems from Area and perimeter: word problems

Question

Skyler climbs a watchtower to guard against forest fires.

\newline

R(h)=\sqrt{13h}

gives the distance, in kilometers, that Skyler can see when their eyes are

h

meters above the ground.

\newline

A(d)=\pi d^{2}

gives the area, in square kilometers, that Skyler can guard when they can see a distance of

d

\newline

Which expression models the area Skyler can guard when their eyes are

h

meters above the ground?

\newline

1

\newline

13\pi h

\newline

13\pi h^{2}

\newline

\sqrt{13\pi h^{2}}

\newline

169\pi h^{2}

Posted 2 months ago

Question

After the outbreak of a mysterious disease, the average wait time at a hospital increased by

70\%

. Before the outbreak, the average wait time at the hospital was

m

\newline

Which of the following expressions could represent the average wait time at the hospital after the outbreak?

\newline

2

\newline

0.7m

\newline

\frac{170}{100}m

\newline

m+70

\newline

m+0.7

\newline

1.7m

Posted 1 month ago

Question

The radius of a semicircle is

3

yards. What is the semicircle's area?

\newline

\pi \approx 3.14

and round your answer to the nearest hundredth.

\newline

Posted 2 months ago

Question

\newline

A man has bent a circular wire of radius

49\text{cm}

to form a square. Find the sides of a square.

\newline

A)100\text{cm}

\newline

B)50\text{cm}

\newline

C)98\text{cm}

Posted 2 months ago

Question

A quarter is worth

\$0.25

and a half dollar is worth

\$0.50

\newline

a. A quarter has a diameter of

\frac{15}{16}

inch and a height of

\frac{1}{16}

inch. Find the surface area of a quarter. Round your answer to the nearest hundredth.

\newline

b. A half dollar has a diameter of

\frac{9}{8}

inches and a height of

\frac{3}{32}

inch. Find the surface area of a half dollar. Round your answer to the nearest hundredth.

Posted 2 months ago

Question

The hypotenuse of a right triangle measures

17 \mathrm{~cm}

and one of its legs measures

8 \mathrm{~cm}

. Find the measure of the other leg. If necessary, round to the nearest tenth.

\newline

\square

\mathrm{cm}

Posted 3 months ago

Question

One of the legs of a right triangle measures

15 \mathrm{~cm}

and its hypotenuse measures

17 \mathrm{~cm}

. Find the measure of the other leg. If necessary, round to the nearest tenth.

\newline

\square

\mathrm{cm}

Posted 3 months ago

Question

One of the legs of a right triangle measures

8 \mathrm{~cm}

and the other leg measures

15 \mathrm{~cm}

. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.

\newline

\square

\mathrm{cm}

Posted 3 months ago

Question

Find the volume of a right circular cone that has a height of

7.4 \mathrm{~cm}

and a base with a radius of

8.1 \mathrm{~cm}

. Round your answer to the nearest tenth of a cubic centimeter.

\newline

\mathrm{cm}^{3}

Posted 3 months ago

Question

Find the volume of a right circular cone that has a height of

13.3 \mathrm{ft}

and a base with a diameter of

9.4 \mathrm{ft}

. Round your answer to the nearest tenth of a cubic foot.

\newline

\mathrm{ft}^{3}

Posted 3 months ago