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
Rina8888 [55]
3 years ago
5

Find the sum of the first four terms of the geometric sequence shown below. 4​, 4/ 3​, 4/9​, ...

Mathematics
1 answer:
user100 [1]3 years ago
3 0
It's evident that the first four terms are 4, 4/3, 4/9, and 4/27. So the fourth partial sum of the series is

S_4=4+\dfrac43+\dfrac49+\dfrac4{27}

It's as easy as adding up the fractions, but I bet this is supposed to be an exercise in taking advantage of the fact that the series is geometric and use the well-known formula for computing such a sum.

Multiply the sum by 1/3 and you have

\dfrac13S_4=\dfrac43+\dfrac49+\dfrac4{27}+\dfrac4{81}

Now subtracting this from S_4 gives

S_4-\dfrac13S_4=4-\dfrac4{81}

That is, all the matching terms will cancel. Now solving for S_4, you
have

\dfrac23S_4=4\left(1-\dfrac1{81}\right)
S_4=6\left(1-\dfrac1{81}\right)
S_4=\dfrac{480}{81}=\dfrac{160}{27}
You might be interested in
What is the sum of the rational expression below? 3x/x+2 + x/x+4
Darya [45]

Ans

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Help!!! Thank you<br> Xxxx
Effectus [21]

Answer: D

Step-by-step explanation:

First I would write out the points of the x and y intercepts and then I would write out an equation in slope-intercept form (y=mx+b). From there I would move my terms accordingly to make it into standard form and compare my answer! Hope this helped!

4 0
3 years ago
Read 2 more answers
What is 4(a5+7)+6(b7-5)
Andrej [43]
4a5+28+6b7-30
4a5+6b7-2<—- this is a to the power of 5 , b to the power of 7
(Is that 5a or a to the power of 5 )
20a+28+42b-30
20a+42b-2<—— this is 5a , 7b
4 0
3 years ago
When solving for the value x in the equation 4(x-1) +6= 18, aaron wrote the following lines on the board:
iren [92.7K]

Answer:

The Distributive Property.

Step-by-step explanation:

4(x - 1) = 12

When distributing out the 4, it must go to all the terms within the brackets like this:

4x - 4 = 12.

4x = 16

x = 4.

8 0
2 years ago
Wserdtcfvygbuhnjkml,;kmojnihbugvyf
Sveta_85 [38]

Answer:

taco

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • If the gradient of a line,C, is 2/3, what is the gradient of a line which perpendicular to C
    6·1 answer
  • HELPPPPP !!!! Answer please and thank you
    14·2 answers
  • RATIO TABLES: An ostrich can run at a rate of 50 miles in 60 minutes. At this rate, how long would it take an ostrich to run 15
    14·1 answer
  • The ideal width of a safety belt strap for a certain automobile is 5 cm. An actual width can vary by at most 0.35 cm. Write and
    12·1 answer
  • If you are smart put this emojiif u not smart put this emoji ok thanks
    13·2 answers
  • (5+4)3=4(3) +5(3) find the property
    10·2 answers
  • Type the missing value<br> K^2+5k+6=(k+2)(k+ )
    11·1 answer
  • HELPPPPPP!! I DONT UNDERSTAND MATHHHHH<br><br> Solve the equation.<br> -2(x+5)=10
    5·2 answers
  • Hoi i need this ✨AnsWeREd✨
    15·2 answers
  • Please help I’m stuck
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!