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
mylen [45]
2 years ago
11

The $23^\text{rd}$ term in a certain geometric sequence is 16 and the $28^\text{th}$ term in the sequence is 24. What is the $43

^\text{rd}$ term
Mathematics
1 answer:
IgorLugansk [536]2 years ago
6 0

By solving a system of equations, we will see that the 43th term of the sequence is 80.3

<h3>How to determine the sequence?</h3>

We know that the n-th term of a sequence is given by:

a_n = a_1*(r)^{n-1}

Here we do know:

a_{23} = 16 = a_1*(r)^{22}\\\\a_{28} = 24 = a_1*(r)^{27}

Basically, we have a system of equations that we can use to find the value of r and the first term of the sequence. If we take the quotient of the two above equations we get:

\frac{24}{16} = \frac{a_1*(r)^{27}}{a_1*(r)^{22}} \\\\1.5 = r^{27 - 22} = r^5\\\\\sqrt[5]{1.5} = r = 1.084

Now we know the value of r, we can use it to find the value of the first term, I will use the first equation:

16 = a_1*(1.084)^{22}\\\\a_1 = \frac{16}{1.084^{22}}  = 2.713

Now we know that the n-th term of our sequence is given by:

a_n = 2.713*(1.084)^{n-1}

Then the 43th term is:

a_{43} = 2.713*(1.084)^{43-1} = 80.3

If you want to learn more about sequences, you can read:

brainly.com/question/7882626

You might be interested in
Hi Help me with question 6b) pls
Romashka-Z-Leto [24]

Answer:

k = 9

Step-by-step explanation:

Consider the pattern on the right side , that is

T_{k} = k(k + 2) + 1 = k² + 2k + 1

Equating

k² + 2k + 1 = 100 ( subtract 100 from both sides )

k² + 2k - 99 = 0 ← in standard form

(k + 11)(k - 9) = 0 ← in factored form

Equate each factor to zero and solve for k

k + 11 = 0 ⇒ k = - 11

k - 9 = 0 ⇒ k = 9

But k > 0 , then k = 9

5 0
2 years ago
How do you do this problems?
rewona [7]

x = 6

Step-by-step explanation:

It's based on similarity of triangles

DEF ~ △XYZ

\implies \mathsf{ \frac{DE }{ XY } =  \frac{EF}{YZ} =  \frac{ FD}{ZX}}

The sides should be taken in order, like the triangles start with DE and XY so, we'll proportionate DE and XY and then the next two sides and so on.

I'm using \mathsf{ \frac{DE }{XY } =  \frac{EF}{YZ} }to get the value of x.

[You can use any two fractions out of the three given above. ]

\implies \mathsf{ \frac{10}{x - 1} =  \frac{8}{4}  }

\implies \mathsf{ \frac{10}{x - 1} =  2  }

\implies \mathsf{ 10 =  2 (x - 1) }

\implies \mathsf{ 10 =  2 x - 2 }

\implies \mathsf{ 10  + 2=  2 x  }

\implies \mathsf{ 1 2=  2 x  }

\implies \mathsf{ x = 6 }

Hence, the value of x is 6.

5 0
2 years ago
Help me pls thxxxxxxxxxx
n200080 [17]

Answer:

brooklyn

Step-by-step explanation:if ur brooklyn do it ur self plese and ty -niki minaj

4 0
3 years ago
Please anwser im having the hardest time on this picture
Free_Kalibri [48]
What you do first is add the books 42 + 85 + 69 which equals 196. Then divide 196 by 7 and you get 28 :)
3 0
3 years ago
Read 2 more answers
Jonathon stated that 0.20 of his coins were quaters. What percentage of jonathons coins are quaters
Anastasy [175]
20%, because 20/100 is equal to 20&.
Hope this helps!
8 0
3 years ago
Other questions:
  • Marcos has $24. Yaneliz has 1/6 of the amount of money Marcos has. Write an expression.
    13·2 answers
  • 3x + 5x = 10 Which problem requires the same strategy (combining like terms)?
    12·2 answers
  • Ms. burke earns $32,000 per year and plans to buy a house. use the banker's rule to determine her maximum allowable mortgage.
    7·1 answer
  • Helpppppplissssssssssss
    10·1 answer
  • Who knows Alot of stuff about Geometry and measurements?
    7·1 answer
  • A professor must randomly select 4 students to participate in a mock debate. There are 15 students in his class. In how many dif
    12·1 answer
  • How do I find angle N? ​
    6·1 answer
  • Add the following numbers and use the checking method (add down and then add up) to make sure your answer is correct. (Copy care
    12·1 answer
  • Pls, look at picture for the question.
    14·2 answers
  • 19=5+7x i need explanation it’s two step equation btw
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!