Find the 6th term of the geometric sequence whose common ratio is 3/2 and whose first term is 6.

Answers

Answer 1

Answer:

The 6th term will be:

[tex]a_6=\frac{729}{16}[/tex]

Step-by-step explanation:

Given

a₁ = 6common ratio r = 3/2

To determine

a₆ = ?

A geometric sequence has a constant ratio r and is defined by

[tex]a_n=a_1\cdot r^{n-1}[/tex]

substituting a₁ = 6, r = 3/2

[tex]a_n=6\cdot \left(\frac{3}{2}\right)^{n-1}[/tex]

Determining 6th term

substituting n = 6 in the given equation

[tex]a_n=6\cdot \left(\frac{3}{2}\right)^{n-1}[/tex]

[tex]a_6=6\cdot \left(\frac{3}{2}\right)^{6-1}[/tex]

    [tex]=6\cdot \frac{3^5}{2^5}[/tex]

    [tex]=\frac{3^5\cdot \:6}{2^5}[/tex]

    [tex]=\frac{3^5\cdot \:2\cdot \:3}{2^5}[/tex]

Cancel the common term

     [tex]=\frac{3^6}{2^4}[/tex]

     [tex]=\frac{729}{16}[/tex]

Therefore, the 6th term will be:

[tex]a_6=\frac{729}{16}[/tex]


Related Questions

Simplify: −5(−4) + 13 =

Answers

Answer:

33

Step-by-step explanation:

-5(-4)= 20

20+13=33

Order from least to greatest.

0.387; 0.3; 0.783; 0.837

Answers

0.3, 0.387, 0.783, 0.837
It would be 0.300, 0.387, 0.783 , 0.837

Hope this helps

Have a great day/night

err i dont know U>U here you go peeps

Answers

Answer:

[tex] {x}^{2} + {y}^{2} + 4x - 2y = - 1 \\ ( {x}^{2}+2\times2\times x + {2}^{2} ) - 4 + ({y}^{2} - 2 \times 1 \times y + {1}^{2} ) - 1 = - 1 \\ {(x + 2)}^{2} - 4 + {(y - 1)}^{2} - 1 = - 1 \\ {(x + 2)}^{2} + {(y - 1)}^{2} = 4\\ {(x + 2)}^{2} + {(y - 1)}^{2} = {( 2) }^{2} [/tex]

Therefore, the centre of the circle is in ( -2, 1 )

and the radius of the circle is 2.

Formula used :-----

[tex] {(x - a)}^{2} + {(y - b)}^{2} = {r}^{2} [/tex]

equation of the circle

where r is the radius of the circle.

(A) 2 is the right answer.

Alicia, Quentin, and Rosalyn are siblings. Alicia is the oldest sibling. Quentin is four years younger than Alicia. Rosalyn is two years older than Quentin. The sum of the siblings’ ages, in years, is 48. How old is Alicia?

Answers

Answer:

Alicia is 18years

Quentin is 14years

Rosalyn is 16years

Step-by-step explanation:

Let the age of Alicia be x

Let the age of Quentin be y

Let the age of Rosalyn be z

If the sum of the siblings’ ages, in years, is 48 then;

x+y+z = 48.... 1

If Rosalyn is two years older than Quentin then;

z =y+2 ..... 2

Also if Quentin is four years younger than Alicia then;

y = x-4 ... 3

From 3:

x = y+4 ... 4

Substitute 2 and 4 into 1 to have:

y+4+y+y+2 = 48

3y + 6= 48

3y = 48-6

3y= 42

y = 14

Since x= y+4

x = 14+4

x = 18

Since z = y+2

z = 14+2

z = 16year

This means that;

Alicia is 18years

Quentin is 14years

Rosalyn is 16years

Find the x- and y-intercepts of
3x – 4y = 24

Answers

y= -6
and
x= 8
i hope that helps :)

Kwan has determined that he can use the expression 2(n+1)−3 to find the number of squares for any step number n. Find an equivalent expression that Kwan can also use. I need help

Answers

Answer:

the answer is 2n-1

Step-by-step explanation:

Answer: 2n-1

Step-by-step explanation:

find the nth term of 8, 2, -4, -10,... then find A50

Answers

Answer:

An=8+(n-1)(-6)

=8-6n+6

=14-6n

A50=14-6(50)

= -286

Find the inverse of function f.
$() = 9x + 7
OA /--) = 7x + 9
OB. 1 (1) = = -1
Oc. 7-1() = -98
OD. () = gr - 1
7

Answers

Answer:

C) f-1(x) = -9x - 7 the inverse of multiplication is division

I need help. For khan academy. Explain if you can

Answers

Answer: Ok so the number on the y axis is 0,-3 cause it is above -4. And the next point is 1,-5. That is because the first thing you plot is the x axis and then the y axis so that it gives you your number

Hey! I need some help with this question I'm not very good with math so if anyone would be willing to help me out id be grateful thx.
An asteroid is 10^{8} miles away from earth, and it is traveling at a speed of 10^{5} miles per day.

How many days will it take the comet to reach earth?

Answers

Answer:

It will take 10^3 days for the comet to reach earth.

Step-by-step explanation:

10^8 = 100,000,000

10^5 = 100,000

100,000,000/100,000 = 1,000

1,000 is equal to 10^3

When adding decimals with the same sign you.....​

Answers

Answer:

keep the decemal in the same place? there's not really alot to go by on your question

Answer:

keep the same sign and add the value to each number

Step-by-step explanation:

Help pls! Extra p! Thank youu

Answers

Answer:

(C) 48 ft^3

Step-by-step explanation:

Volume=L*W*H=6*4*2=24*2=48, making the correct choice (C) 48 ft^3

Term of the arithmetic sequence 12, 10, 8

Answers

Answer:

[tex]\mathtt{\huge\star{\pink{\underline{ 12,\: 10,\: 8,\: 6,\:4,\:2,\:-1,/:-3........ infinite }}}}\huge\star[/tex]

This year is snowed on five of the 12 Days of Christmas! The snowfall amounts were 2
inches, 5 inches, 3 inches, 1 foot and 9 inches. What was the mean amount of snow for
the 12 days? Round your answer to the nearest

Answers

Answer:

Itz 35 i tink

Step-by-step explanation:

umm i god at mafh

What is 4 x 4 x 4 x 4 x 4 x 4 in exponential notation?

Answers

Answer:

[tex]4^{6}[/tex]  

4096

Step-by-step explanation:

i tried

Answer:

[tex]4^{6}[/tex]

Step-by-step explanation:

4 x 4 x 4 x 4 x 4 x 4 it's really just counting how many 4's there are. In this case there are 6 and the number being repeated 6 times is 4 so we only put it as [tex]4^{6}[/tex]. I know I'm late just wanted to answer :'D

HELP I NEED HELP ASAP

Answers

Answer:

Step-by-step explanation:

b

write a linear equation to model the situation. you have walked 4 miles on a trail. you continue to walk at a rate of 3 miles per hour for h hours.

Answers

Answer:

[tex]y= 4 + 3h[/tex]

Step-by-step explanation:

Step one:

Given data

We are given that the initial distance walked is  4 miles

Also, the rate/ speed with which you are currently walking is 3 miles per hour

let the time taken be hours

and let the total distance be y

Step two:

We want to write an expression for the total distance

The total distance is given as

[tex]y= 4 + 3h[/tex]

Find the midpoint of the segment.

A. (1.5, 2)
B. (6, 8)
C. (2, 1.5)

Answers

The answer is A because it’s 1/5

Are the ratios 5:4 and 17:12 equivalent?

Answers

Answer:

yes

Step-by-step explanation:

These fractions are equivalent because they can be divided by the same number... i think

They are not equivalent because if you but them into fractions and divide the numerator by the denominator they do not end up being the same

Please help me with question 4 thank you !!

Answers

Answer:

b) similar by SSS theorem

Step-by-step explanation:

Will give brainliest to a good explanation and some strong evidence to back it up (i rlly need help)

Answers

What are brainliests?
i believe that the answer would be 10 bc 2,4,6,8 and then 12,14,16,18 whatever it was. i think the answer is 10 have a good day

In the diagram if AE = AB, find the area shaded.

Answers

Answer:

Area shaded = 60 [tex]cm^{2}[/tex].

Step-by-step explanation:

From the given diagram,

Area shaded = Area of the trapezoid EBCD

Given that: AE = [tex]\frac{1}{3}[/tex]AB

                        =  [tex]\frac{1}{3}[/tex] x 12    (∵ AB = CD = 12 cm)

                        = 4 cm

                  AE = 4 cm,

Thus,

EB = (12 - 4) cm

    = 8 cm

EB = 8 cm

Area shaded = [tex]\frac{1}{2}[/tex] (EB + CD) x AD

                     =  [tex]\frac{1}{2}[/tex] (8 + 12) x 6

                     = (20) x 3

                     = 60

Area shaded = 60 [tex]cm^{2}[/tex]

The sum of two integers is 5. Their difference is 11. What are
the two integers?

A) 3 and 14

B) -3 and 8

C)2 and 3

D) -14 and - 3

Answers

Answer:a

Step-by-step explanation:

A TV programme begins at 7:45 p.m. and ends 50 minutes later
At what time does it finish?​

Answers

8:35 i think sorry if it’s wrong

A TV programme begins at 7:45 p.m. and ends 50 minutes later.At 8:35 pm time it will finish.

What is an arithmetic operation?

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

It is given that a TV programme begins at 7:45 p.m. and ends 50 minutes later.

Addition is one of the fundamental mathematical operations we utilize on a daily basis. We employ addition of numbers in a variety of contexts. Working with time or money, such as adding up bills and receipts, is one of the most frequent daily uses for adding numbers.

We have to apply the addition operation by splittiong the time as,

=7:45 p.m + 50 minute

=7:45 p.m + 15 minute + 35 minute

=8:00 pm + 35 minute

=8:35 pm

Thus, a TV programme begins at 7:45 p.m. and ends 50 minutes later.At 8:35 pm time it will finish.

Learn more about the arithmetic operation here:

brainly.com/question/20595275

#SPJ2

Which expression uses the associative property to make it easier to evaluate 14(1/7x2/5)?
A. (14x1/7)2/5
B.7(1/14x2/5)
C.(14x5/2)1/7.
D.14(2/5x1/7)​

Answers

Answer:

A

Step-by-step explanation:

Associative property:

(a+b)+c=a+(b+c)

(a*b)*c=a*(b*c)

3^(4x-5) = (1/27)^(2x+10) show your work

Answers

Answer:

3^4x-5=1/27^2x+10

We move all terms to the left:

3^4x-5-(1/27^2x+10)=0

Domain of the equation: 27^2x+10)!=0

x∈R

We get rid of parentheses

3^4x-1/27^2x-10-5=0

We multiply all the terms by the denominator

3^4x*27^2x-10*27^2x-5*27^2x-1=0

Wy multiply elements

81x^6-270x^2-135x^2-1=0

We do not support expression: x^6    

   

Step-by-step explanation:

BRAINLEST TO WHOEVER


X= ?

Answers

Answer:

11.4

Step-by-step explanation:

15 divided by 5= 3 so ABC is 3 times bigger than EFD. you times 3.8 by 3 to get your answer. I hope this helps!!

is x supposed to be z in the dilated shape?

Evaluate (1/3)^3 from Brainly

Answers

Answer:

1/27

Step-by-step explanation:

(1/3)^3 = (1/3)(1/3)(1/3) = 1/(3x3x3) = 1/27

I hope this helped, and if it did, please mark this as brainliest! Thanks!

Answer:

simplified: 1/27

rewritten: 3^-3

Step-by-step explanation:

1. The temperature outside is -5°F.
Name the temperature that would make
the sum of the two temperatures 0°F.
I
Your anstver
Question 2

Answers

Answer:

1

Step-by-step explanation:

Jessica is packing books for her move She has 93 books. Each box can fit 6 books. How many boxes does she need to move all of her books? (Long division please)

Answers

Answer:

16

Step-by-step explanation:

93:6=15.5 As the box can't be half so 16 boxes. In 15 she will pack in each 6 books and in other box 3 books

Answer:

She will need 16 boxes with space for 3 more books

Step-by-step explanation:

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