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
Which equation represents a line that has a slope of 7 and passes through the point of (2,6)?
Strike441 [17]

Answer:

y=7x -8

Step-by-step explanation:

I used desmos but you can also use an equation. I'm sure you're teacher taught you how.

7 0
2 years ago
Read 2 more answers
Taylor writes an expression with 5 terms. All 5 terms are like terms. How many terms are in the equivalent expression with the l
Volgvan
I have no clue I’m dum
7 0
2 years ago
At CD Shack, all used CDs are the same price. Jesse spent $54 and Mimi spent $66 on used CDs. What is the most each used CD coul
Alinara [238K]
Hey there
__________
The correct answer is
Whatever each CD costs, what each person paid is that cost times the number of CDs purchased (no sales tax for this problem).
So, the price of one CD is a factor of $66 (a number of $ that divides $66 evenly).
In theory, it could be $1, $2, $3, $6, $11, $22, $66.
It could even be $0.50, $0.25, $0.20, $0.10, $0.05,...
Also, the price of one CD must be a factor of $54. such as $54,$27,$18,$9,$6,$3,$2,$1,... .
You are looking for the most that price could be.


The grew greatest price that is in both lists is $6.

How can you make those lists?
You can start with the total price, then the price divided by 2, by 3, by whatever whole number you can divide it.

Otherwise, you could find the greatest common factor of 66 and 54
from the prime factorization of both numbers.
___________________
Hope this helps you
5 0
3 years ago
Micah is flying a kite and has used all of the 50 meters of the string. If the kite is 13 meters above the ground, what is the a
Norma-Jean [14]

Answer:

60.0735651 degrees

Step-by-step explanation:

So the hypotenuse is 50 and the vertical leg is 13

For the angle, you need to find the sine (opposite and hypotenuse)

sin(x) = 13/50

x = asin(13/50)

x = 60.0735651

4 0
3 years ago
4. A restaurant charges $9.95 for a large pizza with two toppings, and $1.25 for
bearhunter [10]

Answer:

3 toppings is the answer

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • Write this number in standard form 12 ten thousands,8 thousands,14 hundreds, 7 ones
    5·2 answers
  • Express 4 8\9 as an improper fraction
    8·2 answers
  • 30 Points <br> simplify this fraction <br><br> 5y /23y
    8·2 answers
  • Five less than three times the length, L
    13·1 answer
  • What is the answer for 3,4,5,6 and 7?
    10·1 answer
  • How do i solve this inequality and what is the answer? <br> solve for x: -3x +3 &lt; 6
    9·2 answers
  • What are the solutions
    8·2 answers
  • A Floor is 27 Feet By 12 Feet,What is the square Foot Of that floor?
    6·2 answers
  • Determine which values of p the following integrals converge. Give your answer in each case by selecting the appropriate inequal
    7·1 answer
  • Jeans were $11.50 with a 15% sales tax. What is the sales tax?
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!