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
nlexa [21]
3 years ago
11

Find the sum of the series 9+3+1+........+1/27​

Mathematics
1 answer:
Elina [12.6K]3 years ago
4 0

Answer:

364/27

Step-by-step explanation:

9, 3, 1, ... is a geometric sequence with common ratio r = 1/3.

 

The nth term is a1rn-1.

 

If a1rn-1 = 1/27, then 9(1/3)n-1 = 1/27

 

                                32(3-1)n-1 = 3-3

 

                                3231-n = 3-3

 

                                    33-n = 3-3

 

                                      3-n = -3

 

                                         n = 6

 

The sum, Sn, of the first n terms of a geometric sequence is given by Sn = a1(1 - rn) / (1 - r).

 

So, 9 + 3 + 1 + ... + 1/27 = S6 = 9(1 - (1/3)6) / (1 - 1/3)

 

                                              = 9(1 - 1/729) / (2/3)

 

                                              = (27/2)(728/729) = 364/27

You might be interested in
Twenty less than a number is more than twice the same number . Step by step to get the answer
likoan [24]
20 less than (-20) a number (n) is more than (>) twice the same number (2n)
-20+n>2n
minus n both sides
-20>n
n<-20
3 0
3 years ago
Read 2 more answers
What are all the keys that must be pressed, in correct order, on the calculator shown to find the value of 462 divided by 3?
Alexandra [31]
The second one, 4 6 2 / 3
6 0
3 years ago
Read 2 more answers
Help please thank you!
Maslowich

the error is that they didnt add the exponets

6 0
3 years ago
Please solve this....
ivann1987 [24]

Answer:

the value will be equal to 0

Step-by-step explanation:

see the attached picture for solution --

5 0
3 years ago
This is for my mid term exam review but it’s #2 and it goes with the other question I answered
vodomira [7]

Answer:

B. 8 x 10^3

Step-by-step explanation:

1.6 x 10^5 / 0.2 x 10^2

= 160 000 / 20

= 8 000

You can write this as 8 x 10^3

3 0
2 years ago
Other questions:
  • What is another way to say 345 centimeters?<br><br> 345 cm<br> 345 cg<br> 345 mm<br> 34.5 dl
    7·1 answer
  • I don't really get it. it would be amazing if you help and show work
    5·2 answers
  • What is the laterial area of the cylinder 9 ft 22 ft
    13·1 answer
  • Which of the following numbers are divisible by 3? 225, 8,399, 7,392, 9,830 (can be more than one answer) I'm very busy so I jus
    9·2 answers
  • At top speed, a rabbit can cover 4 miles in 11 minutes. If a
    12·1 answer
  • How does the size of an image compare to the original figure when the original figure undergoes a
    10·1 answer
  • Al bought 24 stickers. He gave away 11 stickers. Then he bought 8 more stickers.
    14·1 answer
  • Simplefly the problem 1/2x/45&gt;61
    7·1 answer
  • Find the derivative of 30x² + 7x at x = 2.
    7·2 answers
  • If = 12 –3 a,find the value ofxwhen a= 8
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!