1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
FinnZ [79.3K]
3 years ago
11

What is the sum of a 7-term geometric series if the first term is -6, the last term is -24,576, and the common ratio is 4?

Mathematics
2 answers:
Zolol [24]3 years ago
7 0

Answer:  The required sum of the given geometric series is - 32766.

Step-by-step explanation:  We are given to find the sum of a 7-term geometric series if the first term is -6, the last term is -24,576 and the common ratio is 4.

We know that,

if 'a' is the first term and 'r' is the common ratio of a geometric series, then its sum up to n terms is given by

S_n=\dfrac{a(1-r^n)}{1-r},~r1.

In the given geometric series,

first term, a = -6  and  common ratio, r = 4.

Since r = 4 > 1, so the sum up to 7 terms is

S_7\\\\\\=\dfrac{a(r^7-1)}{r-1}\\\\\\=\dfrac{-6(4^7-1)}{4-1}\\\\\\=\dfrac{-6(16384-1)}{3}\\\\\\=-2\times 16383\\\\=-32766.

Thus, the required sum of the given geometric series is - 32766.

Zanzabum3 years ago
3 0
<h3><u>Answer:</u></h3>

Hence, the sum of a 7-term geometric series is:

-32766.

<h3><u>Step-by-step explanation:</u></h3>

We have to find the sum of a 7-term geometric series (i.e. n=7) if the first term(a) is -6, the last term is -24,576, and the common ratio(r) is 4.

We know that the sum of the 7-term geometric series is given as:

S_n=a\times (\dfrac{r^n-1}{r-1})

On putting the value of a,n and r in the given formula we have:

S_7=(-6)\times (\dfrac{4^7-1}{4-1})\\\\\\S_7=-32766

Hence, the sum of a 7-term geometric series is:

-32766.

You might be interested in
What is the slope????
murzikaleks [220]

Answer:

-6

Step-by-step explanation:

is that quizzes join lol

8 0
3 years ago
The height and diameter of a cone-shaped storage tank are 9 feet (height) and 14 feet
lana [24]

Answer: 461.60 is the volume of liquid the tank can hold.

Step-by-step explanation:

We were given;

Height H = 9 ft

Diameter D = 14 ft

Pie π = 3.14

We will make use the formula of volume of a cone to get volume of water the tank can hold because it is said that the tank is in the shape of a cone

So

V = 1/3 * πr2h

First we need to find our radius r

Radius = 1/2 of diameter = 14/2 = 7

So using the formula

V = 1/3 * πr2h

V = 1/3 (3.14 * 7² * 9)

V = (3.14 * 49 * 9)/3

V = 1384.74 / 3

V = 461.58 = 461.60 (nearest ten)

3 0
3 years ago
Please help <br><br>must show work<br><br><br>there are 5 that I'm stuck on​
Cloud [144]

you cannot show too much "work"

basically, you remove what is common to all of the factors, and then put brackets, as it will be multiplied back in, remember that when you multiply exponents with the same base, its same as adding them, so subtract to remove...

you can seperate two of the variables , then factor, then subtract the last one from those two, because it cannot be factored out , as in part2 #2

7 0
3 years ago
 PLEASE HELPPPPP ME PLEASE I DONT KNOW WHAT TO DO ☹️#7
nirvana33 [79]

Given:

The function is:

f(x)=-2x+5

To find:

The inverse of the given function, then draw the graphs of function and its inverse.

Solution:

We have,

f(x)=-2x+5

Step 1: Substitute f(x)=y .

y=-2x+5

Step 2: Interchange x and y.

x=-2y+5

Step 3: Isolate variable y.

2y=5-x

y=\dfrac{5-x}{2}

Step 4: Substitute y=g(x).

g(x)=\dfrac{5-x}{2}

Hence, the inverse of the given function is g(x)=\dfrac{5-x}{2} and the graphs of these functions are shown below.

8 0
2 years ago
What is 1481 rounded to the nearest hundred
laila [671]

Answer:

1500

Step-by-step explanation:

1481 to the nearest hundred is 1500 because 8 is nearer to 10

4 0
2 years ago
Read 2 more answers
Other questions:
  • The sale price of these items in a store is 85% of its usual price. A The usual price of a sweatshirt is $18, what is its sale p
    14·2 answers
  • Y=3x+7<br> Y=-7x-4<br> Solve the system
    14·2 answers
  • 1/3 of 12 = 2/3 of ?
    6·2 answers
  • What is the order pair for x+y=4 and x= -1
    14·1 answer
  • A production facility employs 10 workers on the day shift, 8 workers on the swing shift, and 6 workers on the graveyard shift. A
    12·1 answer
  • Convert the following equations from standard form to slope-intercept form.
    13·1 answer
  • 11/16 on a number line that goes from 0-2
    8·1 answer
  • Select all of the attributes of the right rectangular prism.
    5·1 answer
  • How much of the circle is shaded? Write your answer as a fraction in simplest form
    10·2 answers
  • Which of the following sets represent A∩B?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!