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
postnew [5]
2 years ago
13

What is the sum of the first five terms of a geometric series with a1=6 and r=1/3?

Mathematics
1 answer:
Anuta_ua [19.1K]2 years ago
3 0
The sum of a geometric sequence is:

s(n)=a(1-r^n)/(1-r), s(n)=nth sum, a=initial value, r=common ratio, n=term #

In this case we are told that a=6 and r=1/3 so:

s(n)=6(1-(1/3)^n)/(1-1/3)

s(n)=6(1-(1/3)^n)/(2/3)

s(n)=9(1-(1/3)^n), so the sum of the first 5 term is:

s(5)=9(1-(1/3)^5))

s(5)=9(1-(1/243))

s(5)=9(242/243)

s(5)=2178/243

s(5)=242/27

s(5)=8 26/27  ...if you wanted an approximation s(5)≈8.96 to the nearest hundredth...
You might be interested in
La señora Alcántara realiza una compra en el supermercado fortuna, ella solo tiene 12,400 pesos ,compra varios artículos y su co
Aleks [24]

Answer:

She spent = 11560 pesos

Amount left = 840 pesos

Step-by-step explanation:

Mrs. Alcántara makes a purchase at the fortuna supermarket, she only has 12,400 pesos, she buys several items and her purchase is equivalent to 13,600 pesos. How much do you have to pay if they give you a 15% discount? How many was left of what he had in cash?

Amount she has = 12400pesos

Item purchased = 13600 pesos

discount = 15 %

So, the total discount on the item purchased is

= 15 % of 13600

= 0.15 x 13600

= 2040 pesos

So, the amount spent = 13600 - 2040 = 11560 pesos

Amount she left = 12400 - 11560 = 840 pesos

8 0
3 years ago
Identify and explain the error made in the following:<br><br>2x + 8x = 10x^2
Step2247 [10]
It shouldn’t have ^2
8 0
3 years ago
A random sample of 121 automobiles traveling on an interstate showed an average speed of 73 mph. from past information, it is kn
tatiyna

121 is big enough to assume normality and not worry about the t distribution. By the 68-95-99.7 rule a 95% confidence interval includes plus or minus two standard deviations. So 95% of the cars will be in the mph range


(73 - 2 \cdot 11, 73 + 2 \cdot 11) = (51,95)


The question is a bit vague, but it seems we're being asked for the 95% confidence interval on the average of 121 cars. The 121 is a hint of course.


The standard deviation of the average is in general the standard deviation of the individual samples divided by the square root of n:


\sigma = \dfrac{ 11}{\sqrt{121}} = 1


So repeating our experiment of taking the average 121 cars over and over, we expect 95% of the averages to be in the mph range


(73 - 2 \cdot 1, 73 + 2 \cdot 1) = (71,75)


That's probably the answer they're looking for.



4 0
3 years ago
John’s teacher wants to buy giant cookies for the entire class of cookies cost $2.40 each write an equation that shows how many
krek1111 [17]
40 ÷ 2.40= 16.66
the teacher can buy 16 cookies
4 0
2 years ago
What is the value of b in the equation 4b=36
shusha [124]

Answer:

b =9

Step-by-step explanation:

4•9=36

hejsjsjsjsms

3 0
3 years ago
Read 2 more answers
Other questions:
  • The pillars in front of Mr. Jefferson's home are shaped like cylinders. The pillars have a height of 24 ft and a radius of 8 in.
    15·1 answer
  • Suppose there is a 13.4 % probability that a randomly selected person aged 30 years or older is a jogger. In​ addition, there is
    15·1 answer
  • There are 56 fish in a tank and each fish is yellow blue or black.
    7·1 answer
  • Which values are solutions to the inequality below? Check all that apply​
    9·1 answer
  • Identify the y-intercept of the function represented <br> by the following table:
    8·1 answer
  • Relationship between the veriacbles is function of​
    14·2 answers
  • Simply and write in exponential form<br>(1) p2*p-7​
    12·1 answer
  • Can someone help me please !
    14·2 answers
  • £3.23 + £1.47 =
    13·2 answers
  • Multiply. Write your answer in the simplest form. <br> 5 over 2 times 9 over 10
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!