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
After a 75% reduction, you purchase a new clothes dryer on sale for $125. What was the original price of the clothes dryer?
Free_Kalibri [48]
The clothes dryer would've been $500 originally :)
7 0
3 years ago
Find the volume of a cylinder with a diameter of 8 inches and a height that is three times the radius. Use 3.14 for pi and round
ivann1987 [24]
Step 1: Find the area of the base: pi(r^2)=3.14(8^2)=200.96
Step 2: Multiply area by height. Height= 3(8)=24
Volume= 24*200.96=<span>4823.04 inches

Hope this helps!</span>
7 0
3 years ago
Find the value of X.
Vera_Pavlovna [14]

Answer:

x=16

Step-by-step explanation:

(4x+2)+(x+8)=90

5x+10=90

5x=80

x=16

3 0
3 years ago
Show all work. Write the equation in point slope form (5, -9); m = 6
eduard
Point slope form:
y+9=6(x-5)
7 0
2 years ago
Grace rolls a fair, 6-sided die 50 times.
Lostsunrise [7]

Answer:

Step-by-step explanation:

Here's the thing. It is easier to figure out the probability of not getting a six even once during the 50 rolls.

The chance of that happening is (5/6)^50 = 0.00010988

So the probability is succeeding is (1 - 0.00010988) = 0.9999 rounded to 4 places.

5 0
3 years ago
Other questions:
  • Find the arc length function for the curve y = 2x3/2 with starting point p0(25, 250).
    6·1 answer
  • 5/8 divided by 3/2 *2/3
    13·1 answer
  • What are these shapes
    15·1 answer
  • How many grams are in 1,250 kilograms
    14·2 answers
  • Can someone please answer this for me.
    14·1 answer
  • Based on the limited amount of available student parking spaces on the GSU campus, students are being encouraged to ride their b
    9·1 answer
  • Veronica needs to hire carpenters and masons to renovate her house. She needs 9 laborers to finish the work, and has saved $2150
    9·1 answer
  • Which sequence could be partially defined by the recursive f (n + 1) = f(n) + 2.5 for n &gt; 1?
    8·1 answer
  • I need help please. I don’t understand it
    15·2 answers
  • Find five solutions for the linear equations 2x+y=5, and plot the solutions as points on a coordinate plane. Did i do this right
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!