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
MArishka [77]
3 years ago
14

What is the sum of a 7-term geometric series if the first term is −11, the last term is −171,875, and the common ratio is −5?

Mathematics
2 answers:
kipiarov [429]3 years ago
6 0
Answer:

<span>−143231</span>

Explanation:

The general term of a geometric series can be described by the formula:

<span><span>an</span>=a<span>r<span>n−1</span></span></span>

where the initial term is a and common ratio r.

Then we find:

<span><span><span>(1−r)</span><span><span>N∑</span><span>n=1</span></span><span>an</span></span><span><span>=<span><span>N∑</span><span>n=1</span></span>a<span>r<span>n−1</span></span>−r<span><span>N∑</span><span>n=1</span></span>a<span>r<span>n−1</span></span></span><span>=a+<span><span><span>N∑</span><span>n=2</span></span>a<span>r<span>n−1</span></span></span>−<span><span><span>N∑</span><span>n=2</span></span>a<span>r<span>n−1</span></span></span>−a<span>rN</span></span><span>=a<span>(1−<span>rN</span>)</span></span></span></span>

So dividing both ends by <span>(1−r)</span> we find:

<span><span><span>N∑</span><span>n=1</span></span><span>an</span>=<span><span>a<span>(1−<span>rN</span>)</span></span><span>1−r</span></span></span>

In our example, <span>N=7</span>, <span>a=−11</span> and <span>r=−5</span>

So:

<span><span><span><span>7∑</span><span>n=1</span></span><span>(−11)</span><span><span>(−5)</span><span>n−1</span></span></span><span>=
</span></span>
mr_godi [17]3 years ago
4 0
The answer is -143231 
hope this helps:]
You might be interested in
If your target number of calories is 1800 per day to lose weight, but you are consuming 2500 calories per day, then your target
ipn [44]

Answer:

Hi there!

Your answer is:

The target is 72% of what you're currently consuming!

Step-by-step explanation:

2500 cals is 100% of what you're consuming

/2500

1 cals is .04% of what you're consuming

× 1800

1800 cals is 72% of what you're consuming

4 0
3 years ago
Is 4/6 is closer to a whole than 1/2
Andreas93 [3]

Answer:

yes

Step-by-step explanation:

1/2=3/6

4/6=4/6

4/6>3/6

therefore as long as both fractions are less than a whole the bigger the fraction is the closer it is to a whole.

6 0
3 years ago
Read 2 more answers
Jamar has a points card for a movie theater.
netineya [11]

Answer:

He needs to make at least 6 visits.

Step-by-step explanation:

The signing up amount, 20, is a fixed amount.

The amount he receives per movie is 12.5 times the number of visits, v, or 12.5v.

The total amount of points he earns is the sum of the fixed amount and the amount due to the number of visits.

earned points = 12.5v + 20

He must earn 95 points or more.

12.5v + 20 ≥ 95

Subtract 20 from both sides.

12.5v ≥ 75

Divide both sides by 12.5

v ≥ 6

He needs to make at least 6 visits.

8 0
2 years ago
Joe rolls a six sided number cube &amp; flips a coin. what is the probability that he rolls an odd number &amp; flips a head on
creativ13 [48]
3/6 and 1/2. 3/6 is 0.5 and 1/2 is 0.5, 0.5 x 0.5 = 0.25, and 1/4 = 0.25 so it is probably 1/4. Hope it helped if it didn't please let me know and i will corrected my self.
4 0
3 years ago
The average income, I, in dollars, of a lawyer with an age of x years is modeled with the following function: I = -425x^2 + 45,5
lord [1]

We are given

The average income, I, in dollars is

I=-425x^2+45500x-650000

(a)

now, we are given

average income is $275000

so, I=275000

now, we can set them equal

and then we can solve for x

275000=-425x^2+45500x-650000

-425x^2+45500x-925000=0

we will have to use quadratic formula

x=\frac{-45500+\sqrt{45500^2-4\left(-425\right)\left(-925000\right)}}{2\left(-425\right)}:\quad \frac{-\sqrt{45500^2-1572500000}+45500}{850}

x=\frac{-45500-\sqrt{45500^2-4\left(-425\right)\left(-925000\right)}}{2\left(-425\right)}:\quad \frac{\sqrt{45500^2-1572500000}+45500}{850}

we get

x=27.28199

x=79.776

we need to find youngest age

It means that we need to choose smallest value

so,

x=27............Answer

(b)

we are given

x=40

so, we can plug it and find I

I=-425(40)^2+45500(40)-650000

I=490000..............Answer

6 0
3 years ago
Other questions:
  • A system of equations has no solution. If y=8x+7 Is One Of The Equations , Which Could Be The Other Equation?
    8·2 answers
  • A cone and a cylinder have the same bases and volume.How are their heights related? Explain
    8·2 answers
  • 9. The basketball team sold t-shirts and hats at a fundraiser. They sold a total of 23 items and made a
    11·1 answer
  • A bicycle shop marks down each bicycle's selling price b by 24% for a holiday sale. b. What is a single term expression for the
    11·1 answer
  • The difference between two numbers is 9. The first number plus twice the other number is 27. Find the two numbers.
    7·1 answer
  • a long-distance runner passes the 23 km mark of a race in 2 hr 30 min and passes the 44 mark 3 hours later. Assuming a constant
    10·1 answer
  • If a toy rocket is launched vertically upward from ground level with an initial velocity of 120 feet per second, then its height
    10·1 answer
  • Find the area of the white region
    13·1 answer
  • It says 33cm it’s messed up because it’s on a laptop but what’s the volume of this sphere :)
    5·1 answer
  • A train can travel 402 miles on 201 gallons of gas. how far can the train go on 10 gallons?
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!