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?

QUESTION POSTED AT 26/03/2020 - 02:29 PM

Answered by admin AT 26/03/2020 - 02:29 PM

Answer:

Sum of the geometric sequence is 19662.

Step-by-step explanation:

Sum of the terms in a geometric series is represented by the formula

s_{n}=a\frac{(1-r^{n}) }{1-r}

In this formula a = first term

r = common ratio

n = number of terms

Given in the question

a = 6

r = (-4)

n = 7

S_{7}=(6)\frac{[1-(-4)^{7}] }{[1-(-4)]}=6.\frac{(1+16384)}{(1+4)}=\frac{(6)(16385)}{5}= 19662

Therefore sum of the sequence is 19662

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Related questions

At a carnival game, you randomly throw two darts at the board and break two balloons out of 15. What is the probability that both the balloons you break are purple? Write your answer as a fraction or percent rounded to the nearest tenth. (3 red, 4 blue, 2 green, 2 yellow, 4 purple)

Add up the total number of balloons (15) there are 4 purples so the probably of you getting purple at all is 4/15. consider that after you hit the first purple, your odds decrease to 3/14. 

ANSWERED AT 28/03/2020 - 01:00 PM


QUESTION POSTED AT 28/03/2020 - 01:00 PM

Need help on number 4. Complete Sentences Please! Thank you, ✨

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ANSWERED AT 28/03/2020 - 12:59 PM


QUESTION POSTED AT 28/03/2020 - 12:59 PM

If the measure of angle 4 is 132°, what is the measure of angle 7?

Angles 1, 3, 5, 7, 9 and 11 are corresponding while angles 2, 4, 6, 8, 10 and 12 are corresponding
angles 8 and 7 are supplementary
since 4 and 8 are corresponding, angle 4 is 132° so angle 8 would also be 132°
180-132=48
°
angle 7 would be 48
°

ANSWERED AT 28/03/2020 - 12:55 PM


QUESTION POSTED AT 28/03/2020 - 12:55 PM

Given points A(4,5) and B(-4,11). Find the distance AB to the nearest tenth.

If A(x', y') & B(x",y") the the distance AB is given by the following formula:

AB =√[(x"-x')² + (y"-y')²]

Plug into the above with A(4,5) and B(-4,11).

AB =√[(-4-4)²+(11-5)²] =√(-8)²+(6)² = √(64) + (36) =√100 = 10

ANSWERED AT 28/03/2020 - 12:55 PM


QUESTION POSTED AT 28/03/2020 - 12:55 PM

Two less than 6 times the difference of 9 and 5

X=6(9-5)-2
So
X=6(4)-2
X=24-2
X=22

ANSWERED AT 28/03/2020 - 12:52 PM


QUESTION POSTED AT 28/03/2020 - 12:52 PM

(i3)^2(-i0)^3(3i2)^4

The answer is 0 is this if i stands for a square root.
The answer is -81 if i is a variable.

ANSWERED AT 28/03/2020 - 12:51 PM


QUESTION POSTED AT 28/03/2020 - 12:51 PM

The lengths of three sides of a triangle are given. Determine whether each triangle is a right triangle. 1. 14 m, 5 m, 4 m 2. 3 in., 4 in., 5 in. Are these right triangles?

In a right triangle, the hypotenuse is always the longest side.  Plus, the hypotenuse squared has to equal the sum of the squares of the other 2 sides.  For the first "triangle" above: does 14 ^{2} =5 ^{2} +4 ^{2} ?  Let's check.  196 = 25 + 16 so does 196 = 41?  Obviously not.  So that is not a right triangle.  Let's check the second one the same way.  Does 5 ^{2} =3 ^{2} +4 ^{2} ?  25 = 9 + 16.  Does 25 = 25?  Of course it does!  So 1 is not a right triangle, but 2 is!

ANSWERED AT 28/03/2020 - 12:48 PM


QUESTION POSTED AT 28/03/2020 - 12:48 PM

A bag of coins contains 2 quarters, 5 dimes, 3 nickels, and 4 pennies. If 2 coins are randomly chosen from the bag, one after the other, and not replaced, and if the total value of the chosen coins is 26 cents, what is the probability that a third coin randomly chosen from the bag will be a penny?

Answer:

B

Step-by-step explanation:

The 2 coins that have a combined value of 26 cents are a quarter and a penny. That means that 1 quarter and 1 penny must have already been removed from the bag. For this reason, the bag now contains 1 quarter, 5 dimes, 3 nickels, and 3 pennies. Therefore, the probability that a third coin randomly chosen from the bag will be a penny is

3

1 + 5 +3 + 3

=

3

12

=

1

4

.

ANSWERED AT 28/03/2020 - 12:47 PM


QUESTION POSTED AT 28/03/2020 - 12:47 PM

What are the intercepts of 6x + 8y = 24? a.(4, 0) and (0, 1) b.(12, 0) and (0, 1) c.(3, 0) and (0, 4) d.(4, 0) and (0, 3)

6x + 8y = 24

x intercept is the value when y =0 & y intercept is the value when x=0


for y=0 ==> 6x+0 =24 ==> x=4 for x=0==> 0+8y =24 ==> y=3

(4,0) & (0,3) (ANSWER d)

ANSWERED AT 28/03/2020 - 12:46 PM


QUESTION POSTED AT 28/03/2020 - 12:46 PM

Joe has two empty boxes, one box is 15 inches wide, 20 inches long and 10 inches high. The second box has the same length and width but is 4 inches taller. How much additional spaces is in the box

Space in the box = volume
volume = length x width x height
box 1 volume = 15 x 20 x 10 = 3000
box 2 volume = 15 x 20 x 14 = 4200
how much space is left = box 2 - box 1 = 1200 inches

ANSWERED AT 28/03/2020 - 12:44 PM


QUESTION POSTED AT 28/03/2020 - 12:44 PM

Is 24 to 26equivalent ratios??

No it is not equivalent

ANSWERED AT 28/03/2020 - 12:44 PM


QUESTION POSTED AT 28/03/2020 - 12:44 PM

What is 6(x+4)? Show work

You would multiply 6 by both, the x and the 4 to get your answer.
6(x+4)
6*x+6*4=
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ANSWERED AT 28/03/2020 - 12:43 PM


QUESTION POSTED AT 28/03/2020 - 12:43 PM

A box of 6 coins (penny, nickel, dime or quarter) worth $0.67 is shaken. What is the probability that a nickel is drawn first and then a quarter? Assume no replacement and that all coins are equally likely.

Answer:

There is a 6.67% probability that a nickel is drawn first and then a quarter.

Step-by-step explanation:

There are 6 coins. The sum of their values is $0.67. We need to find how many of each coin are there.

A penny is worth 1 cent.

A nickel is worth 5 cents.

A dime is worth 10 cents.

A quarter is worth 25 cents.

To get to 67 cents, we need:

Two pennies, a nickel, a dime and two quarters.

So:

What is the probability that a nickel is drawn first and then a quarter? Assume no replacement and that all coins are equally likely.

Initially there are 6 coins, of which 1 is a nickel. So the probability that the nickel is drawn is:

P_{1} = \frac{1}{6}

There are no replacements, so now there are 5 coins, of which 2 are quarters. So the probability that a quarter is drawn is:

P_{2} = \frac{2}{5}.

The probability that a nickel is drawn first and then a quarter is:

P = P_{1}*P_{2} = \frac{1}{6}{2}{5} = \frac{1}{15} = 0.0667

There is a 6.67% probability that a nickel is drawn first and then a quarter.

ANSWERED AT 28/03/2020 - 12:42 PM


QUESTION POSTED AT 28/03/2020 - 12:42 PM

Which of the equations has a solution of 7. y - 41 = 48 m + 6= 1 z - 2 = 5 n + 50 = 30

The answer to th question is 7.

ANSWERED AT 28/03/2020 - 12:42 PM


QUESTION POSTED AT 28/03/2020 - 12:42 PM

Which of the equations has a solution of 7. y - 41 = 48 m + 6= 1 z - 2 = 5 n + 50 = 30

The third one because you plug 7 in for z
Z-2=5 turns into 7-2=5 which is true

ANSWERED AT 28/03/2020 - 12:42 PM


QUESTION POSTED AT 28/03/2020 - 12:42 PM

Rewrite the fraction as a decimal. ​​​69 _ 4 ​​ Simplify plz!

The answer would be 17.25

ANSWERED AT 28/03/2020 - 12:38 PM


QUESTION POSTED AT 28/03/2020 - 12:38 PM

True or False? The sum of the differences must be zero for any distribution consisting of n observations.

Answer:

it's right, it's true

Step-by-step explanation:

ANSWERED AT 28/03/2020 - 12:37 PM


QUESTION POSTED AT 28/03/2020 - 12:37 PM

(08.01)Consider the following system of equations: y = 5x + 6 y = −x − 7 Which description best describes the solution to the system of equations?

If you want an answer to question: You can make the equations equal to each other and solve for x. So, since the y values are the same, we can do 
(+x)5x+6 = -x-7. (+x)
(-6)6x+6= -7(-6)
  (1/6) x 6x= -13 x (1/6)
x= -13/6
Substitute −13/6 for x in y=5x+6:
y=5x(−13/6) + 6
y = -29/ 6.
y= -29/6  and x= -13/6
 

ANSWERED AT 28/03/2020 - 12:37 PM


QUESTION POSTED AT 28/03/2020 - 12:37 PM

You jog 6 and 2 thirds miles around a track each day. If you jogged that distance 4 times last week, how many miles did you jog?

Multiply 2/3 by 4 to get a total jogging distance of 8/3 miles. Convert it to a mixed number, and your answer will be 2 1/3 miles.

ANSWERED AT 28/03/2020 - 12:36 PM


QUESTION POSTED AT 28/03/2020 - 12:36 PM

Theo builds the first layer of a rectangular prism using 4 unit cubes. he adds 3 more layers of 4 unit cubes each. how many unit cubes does he use for the prism?

First you multiply 3 and 4 to get 12, then add 4 to get 16. There is also another way to do it you can draw a picture of 4 blocks then add 3 more of the 4 blocks then add one more of the 4 blocks to get 16. 16 is the answer! Hope this helped ( :

ANSWERED AT 28/03/2020 - 12:36 PM


QUESTION POSTED AT 28/03/2020 - 12:36 PM

What is the least common multiple of 4 and 8

8 is the least common mutlible of4 and 8
8:   2224:   22 LCM:   222

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ANSWERED AT 28/03/2020 - 12:35 PM


QUESTION POSTED AT 28/03/2020 - 12:35 PM

Quadrilateral ABCD is a parallelogram with AB = 3y – 6, BC = 5x – 8, CD = 2y + 4, and AD = 4x –1. Find x. A. 7 B. 14 C. 27 D. 28

Choice A. Work done below:
4x-1=5x-8 ( Set the opposite sides equal to each other).
4x-5x-1=-8 (Subtract 5x on both sides)
-x-1=-8 (Combine like terms)
-x=-8+1( Add 1 on both sides)
-x=-7 (Now since you have a negative sign on both sides you can cancel them)
x=7 ( Making that as your answer!!)

ANSWERED AT 28/03/2020 - 12:33 PM


QUESTION POSTED AT 28/03/2020 - 12:33 PM

The first three terms of a geometric sequence are shown below. What is the eighth term of the sequence? A. -128x^8-384x^7 B. 128x^8+384x^7 C. 256x^9+768x^8 D. -256x^9-768x^8

Answer:

Option A is correct.

Step-by-step explanation:

Given:

First term, a = x + 3

second term = -2x² - 6x

Third term = 4x³ + 12x²

Common ratio, r = \frac{-2x^2-6x}{x+3}=\frac{-2x(x+3)}{x+3}=-2x

nth term of GP is gievn by, a_n=ar^{n-1}

So, Eight term = a_8=(x+3)(-2x)^{8-1}=(x+3)(-2x)^{7}=-128x^8-384x^7

Therefore, Option A is correct.

ANSWERED AT 28/03/2020 - 12:31 PM


QUESTION POSTED AT 28/03/2020 - 12:31 PM