Consider the following sequence
152, -76, 38, -19
Write a rule for the nth term and then find [tex]a_7[/tex]

Answers

Answer 1

Answer:

a₇ =  2.375

Step-by-step explanation:

There is a common ratio r between consecutive terms, that is

r = [tex]\frac{-76}{152}[/tex] = [tex]\frac{38}{-76}[/tex] = [tex]\frac{-19}{38}[/tex] = - [tex]\frac{1}{2}[/tex]

This indicates the sequence is geometric with nth term

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

Here a₁ = 152 and r = - [tex]\frac{1}{2}[/tex] , then

[tex]a_{n}[/tex] = 152 [tex](-\frac{1}{2}) ^{n-1}[/tex] , so

a₇ = 152 [tex](-\frac{1}{2}) ^{6}[/tex] = 152 × [tex]\frac{1}{64}[/tex] = 2.375

Answer 2

Answer:

Solution given:

first term [a]=152

second term[b]=-76

common ratio[r]=[tex] \frac{-76}{152}[/tex]=-1/2

now

for nth term ,we have

nth term =a [tex] {r}^{n -1} [/tex]

now

7th term==152[tex] {-1/2}^{7 - 1} [/tex]

=152×1/64=19/8


Related Questions

The probability of choosing a blue marble from a bag is 5/12 and a yellow marble 1/3. What is the probability of not choosing one of these marbles?

Answers

Answer:

1/20

Step-by-step explanation:

Simple probability is found by counting all the results which fit requirements and dividing by all possible results.

To find probability of two results in a row, multiply chance of first result by chance of second result.

Since you are replacing the marble before the second draw, we don’t have to figure out the various changes in odds for the different possible first draws. It’s just that simple.

There are 5 black marbles

There are 4 red marbles

There are always 20 marbles in all

5/20*4/20=1/4*1/5=1/20

By coincidence, the same as the chance of drawing the white marble in one draw.

If the number of students who participated in art decreased by 5, how many total students would the principal have expected in order to keep the number of students who participated in art proportional to the total number of students surveyed? ​

Answers

Answer: There isn’t enough context.?

Step-by-step explanation:

HELP ME PLEASEEEEEEEEEEEE

Answers

Should be D. if I'm correct. This pair of angles doesn't seem to be in the right position to form a 90 degree or a 180 degree angle, ruling out supplementary and complementary angles, and they definitely aren't vertical angles, leaving only choice D: None of the above.

Otis has saved $18,500 so far to buy a
house. He can put this amount into an
account that earns 5.1% simple interest,
or another with 5.1% compounded
annually. Which method of earning
interest should he choose, simple or
compound, and how much more interest
will the account earn using that method
after 4 years?
F Compound interest; $15,106.30
G Simple interest; $15,106.30
H Simple interest; $298.65
J Compound interest; $298.65
no

Answers

9514 1404 393

Answer:

  J Compound interest; $298.65

Step-by-step explanation:

Interest compounding pays interest on the interest. For the same annual rate, any amount of compounding will earn more interest.

For short time periods, the effect of compounding is not great. In general, it will be a fraction of the equivalent simple interest rate. Here, the effective multiplier for annual compounding is ...

  1.051^4 = 1.22024337

and the effective multiplier for simple interest is ...

  1 +0.051·4 = 1.204

Then the difference in interest rate multiplier for the 4-year period is ...

  1.22024337 -1.204 = 0.01614337

That fraction of the $18500 principal is $298.65.

Compound interest earns $298.65 more than simple interest in this scenario.

5, 5 ,8 ,8 ,8, 9, 17, 19, 19, 19, 19, 22, 28

What are the median and mode?

Answers

Answer:

the median is 17  the mode is 19

Step-by-step explanation:

17 is in the middle with 6 on each side so it is the median

19 occurs most often so it is the mode

Determine whether or not the triangle with the given side lengths is a right triangle.
60 inches, 11 inches, 61 inches
leg a
in
leg b =
in
hypotenuse c =
in
Right triangle? Yes or No.

Answers

I would say no because I think the highest corner degree would be 79 degrees and a right triangle needs to be 90 degrees. Sorry if it’s wrong.

Please answer the following question

Answers

Answer:

first give options it is very hard to do

please help ! no links please

Answers

All triangles must have angles that add up to the same amount of degrees, so if the two triangles share one exact point, it is assumed that those angles would be the same. Basically just use the fact that the sides are the same and marked by dashes, and the missing line can be proven with the use of the angles that are in between the point that both share.

Can I have some help please.

Answers

Answer:

with?

Step-by-step explanation:

...............................................

Question 4 of 10
Suppose that many large samples are taken from a population, and the
sample proportions center around 0.58. Which of the following is most likely
to be the population parameter?
O A. 0.68
OB. 0.58
O C. 0.78
O D. 0.48

Answers

Answer:

A- 0.68

Step-by-step explanation:

0.58 is most likely to be the population parameter, since the sample proportions center around this value.

Option B is the correct answer.

We have,

When many large samples are taken from a population, the sample proportions should converge to the population proportion.

If the sample proportions center around a certain value, that value is likely to be a good estimate of the population proportion.

In this case,

Since the sample proportions center around 0.58, it is likely that the population proportion is also around 0.58.

Therefore,

0.58 is the most likely population parameter.

Learn more about population parameters here:

https://brainly.com/question/30689789

#SPJ7

2. Given log35 = 1.465, approximate the value of log325.

Answers

9514 1404 393

Answer:

  2.930

Step-by-step explanation:

The applicable rule of logarithms is ...

  log(a^b) = b·log(a)

___

Here, this means ...

  [tex]\log_3(25)=\log_3(5^2)=2\cdot\log_3(5)=2\cdot1.465\\\\\boxed{\log_3(25)=2.930}[/tex]

what is the measure of angel R ? pls i need help​

Answers

Answer:

40

Step-by-step explanation:

(120 - 40)/2 = 80/2 = 40


A line passes through the point (8, -7) and has a slope of
3/4
Write an equation in slope-intercept form for this line.

Answers

Answer:

y = 3/4x - 13

Step-by-step explanation:

As we already know the slope, we just need to find the y-intercept.

y = 3/4x +b

-7 = 3/4(8) + b

-7 = 6 + b

-13 = b

y = 3/4x - 13

please help me with this math problem, the question is on the picture that i attached, ill mark brainliest if the answer is correct. NO links!

Answers

Answer:

cos 29 = x / 11

11 * cos 29 = x

x =  11 * 0.87462

x = 9.62082

Step-by-step explanation:

what are the factors of 30 that have a sum of -11

Answers

Answer:1, 2, 3, 5, 6, 10, 15, 30.

Step-by-step explanation:

What’s the answer for both ASAP

Answers

Answer:

Step-by-step explanation:

1. 1.643

2. -0.03

What is a simpler form of (3x+1)(x+4) ?

Answers

Answer:

That is the simplest form.

Step-by-step explanation:

[tex]3x^2+13x+4[/tex] = (3x+1)(x+4)

Answer:

The equation is already simplified!

Step-by-step explanation:

credits to the user jlinnartz for pointing out my mistake! kudos to the explanation above!!! :)

visitors spend 1/3 of their time waiting in line for rides. Of the santos family spends 53/4 hours at the park how long do they wait in line

Answers

Answer: 1 11/12 hours

Step-by-step explanation:

Since visitors spend 1/3 of their time waiting in line for rides and the Santos family spends 5¾hours at the park.

The tune spent waiting in line will be calculated by multiplying ⅓ by 5¾. This will be:

= ⅓ × 5¾

= ⅓ × 23/4

= 23/12

= 1 11/12 hours

Therefore, they'll wait in the park for 1 11/12 hours

4, Give a pair of inequalities that describes
the set of all points in the first quadrant​

Answers

Answer:

x > 0

y > 0

Step-by-step explanation:

The first quadrant is the quadrant formed by the positive x-axis and the positive y-axis.

And we know that all the elements in this quadrant are larger than zero.

Then, a point (x, y) is on the first quadrant only if:

x > 0

y > 0

Note that we ignore the points with x = 0 or y = 0, this is because these points are shared between quadrants, and these points are not defined as belonging to any quadrant.

Let a1, a2 and a3 be as in (a). Let a4 =   1 4 −5  . Without doing any further calculations, find all values of t for which there will be a unique solutions to a1y1 + a2y2 + a3y3 + a4y4 = c for every vector c in R 3 . Explain your answer

Answers

Answer:

Hello your question is incomplete attached below is the complete question

a) attached below

b ) Vectors a1 and a2 are linearly independent  and this is because they are a scalar multiple of each other

c)  There are 3 equations and 4 unknown hence for any t value there will be a solution

Step-by-step explanation:

A) attached below

b) Vectors a1 and a2 are linearly independent  and this is because they are a scalar multiple of each other

C) there are 3 equations and 4 unknown hence for any t value there will be a solution

Find the quotient. Write your answer in scientific notation, (3.6 x 10 to the power of 7) divided by (7.2 times 10 to the 7)

Answers

Given:

The given expression is:

[tex]\dfrac{3.6\times 10^7}{7.2\times 10^7}[/tex]

To find:

The value of the quotient.

Solution:

We have,

[tex]\dfrac{3.6\times 10^7}{7.2\times 10^7}[/tex]

It can written as:

[tex]=\dfrac{3.6}{7.2}\times \dfrac{10^7}{10^7}[/tex]

[tex]=\dfrac{1}{2}\times 1[/tex]

[tex]=0.5[/tex]

It can be rewritten as:

[tex]=5\times \dfrac{1}{10}[/tex]

[tex]=5\times 10^{-1}[/tex]

Therefore, the value of the quotient is [tex]5\times 10^{-1}[/tex].

Which expression is equivalent to 2(3g-4) - (8g+3)?

Answers

Answer:

I think -2g+5

Step-by-step explanation:

its distributive property and adding... hope this helped

Can someone help me with this?

Answers

Increasing at a decreasing rate.

Graph the equation in a online graph and see how the line looks and compare with the picture attached.

Please help I can’t fail this

Answers

The answer is B) y = 1.5x + 5

Answer:

B

Step-by-step explanation:

I plugged it into a graphing calculator but if you use "rise over run" you'll get your answer without a phone

looking for a friend to meet and get to know :)

Info 99423608632
pass Bz9A3w

Answers

Step-by-step explanation:

flw me. plzzzzzzzzzzzzzzzzzz

Answer:

um.... ok, thanks 4 tho points tho..

Step-by-step explanation:

Sally paid $1.50 for pounds of apples at the Grocery Mart. Fred paid $1.95 for 3 pounds of apples at the Corner Fruit Stand. How much did Sally pay per pound of apples? (enter in the format of money, do not use the $ sign) Answer value'

Answers

Part A: Sally paid less money per pound than Fred did

Part B: John paid $3.58 for 5.5 pounds of apples at the Grocery Mart

Part C: y = 0.65x

Step-by-step explanation:

Part A:

Sally: 1.5/2.5 = x/1

cross multiply: 2.5x = 1.5*1

simplify: 2.5x = 1.5

divide both sides by 2.5: x = 0.6

Fred: 1.95/3 = x/1

cross multiply: 3x = 1.95*1

simplify: 3x = 1.95

divide both sides by 3: x = 0.65

Fred paid 65¢/pound while Sally paid 60¢/pound

Part B:

price/pound*amount John bought: 0.65/1 = x/5.5

cross multiply: 1x = 0.65*5.5

simplify: x = 3.575

Part C:

y = 0.65x

Fred wants to put a carpet in this room. The carpet costs $15.00 a square yard, how much would it cost for a 3 ft by 6 feet by 9ft by 12 ft

Answers

Solution :

Cost of carpeting per square yard = $ 15.00

For 3 ft by 6 ft

1 yard = 3 feet

∴ 1 feet =  [tex]$\frac{1}{3}$[/tex] yard

So,

Therefore, area of 3 ft by 6 ft is = [tex]$3 \times \frac{1}{3} \times 6 \times \frac{1}{3} $[/tex]

                                                    = 1 x 2

                                                    = 2 square yard

Therefore, cost of carpeting 2 square yard = 2 x 15

                                                                       = $ 30

For 9 ft by 12 ft

1 yard = 3 feet

∴ 1 feet =  [tex]$\frac{1}{3}$[/tex] yard

So,

Therefore, area of 9 ft by 12 ft is = [tex]$9 \times \frac{1}{3} \times 12 \times \frac{1}{3} $[/tex]

                                                    = 3 x 4

                                                    = 12 square yard

Therefore, cost of carpeting 2 square yard = 12 x 15

                                                                       = $ 180

Help me with the correct answer please

Answers

Step-by-step explanation:

Since, The formula of Pythagoras is A² + B² + C²

(therefore)* let A be 8 mm

B be 6 mm

Therefore, 8² + 6² = 64 + 36

= 100

= 10( after squaring it )

Hope it helps,if it is correct like and mark me.

please help meeeeeeeee

Answers

Answer:

Ues math w/a/y

Step-by-step explanation:

ues it

11. What is the value of x?

A 48
B 30
C 60
D 36

Answers

Answer:

I think it is B

hope this helps

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