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
Alisiya [41]
3 years ago
11

Find all geometric sequences such that the sum of the first two terms is 24 and the sum of the first three terms is 26.

Mathematics
1 answer:
Serga [27]3 years ago
6 0

Answer:

<h3>The nth term Tn = -8(-1/4)^(n-1) or Tn = 6(1/3)^(n-1) can be used to find all geometric sequences</h3>

Step-by-step explanation:

Let the first three terms be a/r, a, ar... where a is the first term and r is the common ratio of the geometric sequence.

If the sum of the first two term is 24, then a/r + a = 24...(1)

and the sum of the first three terms is 26.. then a/r+a+ar = 26...(2)

Substtituting equation 1 into 2 we have;

24+ar = 26

ar = 2

a = 2/r ...(3)

Substituting a = 2/r into equation 1 will give;

(2/r))/r+2/r = 24

2/r²+2/r = 24

(2+2r)/r² = 24

2+2r = 24r²

1+r = 12r²

12r²-r-1 = 0

12r²-4r+3r -1 = 0

4r(3r-1)+1(3r-1) = 0

(4r+1)(3r-1) = 0

r = -1/4 0r 1/3

Since a= 2/r then a = 2/(-1/4)or  a = 2/(1/3)

a = -8 or 6

All the geometric sequence can be found by simply knowing the formula for heir nth term. nth term of  a geometric sequence is expressed as

if r = -1/4 and a = -8

Tn = -8(-1/4)^(n-1)

if r = 1/3 and a = 6

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

The nth term of the sequence above can be used to find all the geometric sequence where n is the number of terms

You might be interested in
Matthew has 8 pencils.three of them do not have erasers on the end .what is the fraction on the pencil do not have erasers of th
Diano4ka-milaya [45]
The answer is 3/8 because 3 out of the 8 don't have erasers.


3 0
3 years ago
Read 2 more answers
Which statement describes the graph of f(x)=-4x^3-28x^2-32x+64
lord [1]
The only that has the shape of the one below.

y = -4(x^3 + 7x^2+8x - 16)
Let x = 1
y = - 4(1 + 7 + 8 - 16)
y = 0

y = -4(x -1)(x^2 + 8x + 16)
y = -4(x - 1)(x + 4)^2


7 0
3 years ago
Read 2 more answers
Please answer very quickly
PolarNik [594]

Answer:

ABD

Step-by-step explanation:

3 0
2 years ago
What does 19.2 x 29.5 equal? Step by step instructions please
slava [35]

Answer:

566.4

Step-by-step explanation:

do multipilication

5 0
2 years ago
Read 2 more answers
Find the diameter of a circle with an area of 4π in 2<br><br><br>Please help!
Mazyrski [523]

Answer:

I just wanted to set positive vibes!!!!!

Step-by-step explanation:

these times are very hard and are sending negative vibes and I just want you to know I love you

7 0
3 years ago
Read 2 more answers
Other questions:
  • MAJORR HELP!!
    10·1 answer
  • Surface Area Rectangular Prism
    10·2 answers
  • a drawer contains 9 white paper clips, 5 green paper clips, and 6 red paper clips. One paper clip is selected at random. What is
    6·2 answers
  • Write an equation in point-slope form for each line.<br> (If possible please show work)
    7·1 answer
  • Isaac can text 96 words in 6 minutes. At this rate, how many words could he text in 10 minutes?
    11·1 answer
  • What is 2.34 as a fraction and precent?
    8·1 answer
  • What's the slope- intercept equation? 10x-3y= -6
    13·1 answer
  • What is the answer to 5-10x&lt;-145
    9·1 answer
  • What is the mean of 9, 25, and 53?<br><br> 3<br><br> 9<br><br> 25<br><br> 29
    14·2 answers
  • Find the missing side length in the image below 12 18 and 10
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!