A sequence has an initial value (I) of -17 and its fourth term (a4) is 35. What is its general equation? Its 14th term?

Also, A sequence has a CR of 4/5 and its eighth term (a8) is (393216/3125). What is its general equation? Its 3rd term?

Answers

Answer 1

Answer:

The sequence is an Arthemtic Progression

An=A1+(n-1)d

A1 is first term, An is nth term, n is number of term, and d is common difference

therefore

A4=35, A1= -17

A4=A1+(4-1)d

35= -17+3d

35+17=3d

52=3d

52/3=3d/3

14=d

common diffrence(d)=14

The general solution is given by

An= -17+(n-1)14

An= -17+14n-14

An= -31+14n

An= 14n-31

A14 term, means n=14

From An=A1+(n-1)d

A14= -17+(14-1)14

= -17+(13×14)

= -17+182

= 165.

Therfore, the 14th term is 165.

2. A sequence has a CR of 4/5 and its eighth term (a8) is (393216/3125). What is its general equation? Its 3rd term?

solution

common ratio(r)=4/5

eighth term(G8)=393216/3125

From Gn= G1r^(n-1)

G8 means n=8

G8=G1r^(n-1)

393216/3125=G1(4/5)^(8-1)

393216/3125=G1(4/5)^7

G1=(393216/3125)/(4/5)^7

G1=600

The first term is given by G1=600

Therefore

The General equation is given by

The General equation is given by Gn= 600(4/5)^(n-1)

3rd term (G3)

G3= G1(4/5)^(3-1) where n=3,

=600(4/5)^2

=600(16/25)

=384

Therefore, the 3rd term is given by G3= 384.

I have made some Corrections i messed up somewhere.


Related Questions

What is the equation of the line?

Answers

Answer:

I believe it should be the second answer

Mr. Lee is a hotdog and drink vendor at a baseball game. Hot dogs are 3.50 and drinks are 1.50. If Mr. Lee sold enough to make 450 dollars on Monday. He remembers that on Monday he sold three times as many drinks as he did hot dogs. How many hot dogs and how many drinks did Mr. Lee sell on Monday?

Answers

Answer:

33 hotdogs and 225 drinks on Monday

Step-by-step explanation:

We would use the ratio of 1:3 hotdogs to drinks

Split the ratio in 450 and we get 112.5:337.5

$112.5 would be the earnings of hotdogs

$337.5 would be the earnings of the drinks

Now we divide each individually by its cost

$112.5/3.5

= 32 1/7,

$337.5/1.5

= 225

We will round the hotdogs to 33 as the word problem says "sold enough to make."

Find the slope of the line without graphing using the 2 points below.



(-3 , 4) & (13 , 8)



m = _______

Answers

Answer:

Step-by-step explanation:

1. use the slope formula --> (y2-y1)/(x2-x1)

2. (8 - 4)/(13 -(-3))

3. 4/16

4. m = 1/4

A box of cereal states that there are 90 calories in a 3 4​-cup serving. What is the unit rate for calories per​ cup? How many calories are there in 2 cups of the​ cereal?

Answers

Answer:

Calories per cup = 120 calories

Calories in 2 cups = 240 calories

Step-by-step explanation:

Given that:

Number of calories in a [tex]\frac{3}{4}^{th}[/tex] cup serving = 90 calories

To find:

Unit rate for calories per cup = ?

Number of calories in 2 cups of cereal = ?

Solution:

Here we are given the number of calories in a [tex]\frac{3}{4}^{th}[/tex] cup serving.

To find the calories in one cup, we need to divide 90 calories with [tex]\frac{3}{4}[/tex].

So, unit rate for calories per cup can be given as:

[tex]\dfrac{90}{\frac{3}4}\\\Rightarrow \dfrac{90}{3}\times 4\\\Rightarrow \bold{120 \ calories}[/tex]

To find the calories in 2 cups of cereal, we need to multiply the unit rate for calories per cup with 2.

So, calories in 2 cups of cereal = [tex]120 \times 2[/tex] = 240 calories

Therefore, the answer is:

Calories per cup = 120 calories

Calories in 2 cups = 240 calories

Please help! Its algebra 2

Answers

Answer:

Step-by-step explanation:

1. factor completely

5. simplify first fraction

4. common denominator

2 add the fractions

3. open paranthesis and combine like terms

which quadrant will be completely shaded by the graph of 2x+3y ≥-6

Answers

Answer:

quadrant I

Step-by-step explanation:

21. M List the sides of ABC in order from shortest to
longest

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Answer:

Ummm... I think it would help if you take a screen shot

Step-by-step explanation:

Answer:

The sum of all angles is 180degrees

100 = 8x +4

X =( 100-4)/8 =12

A = 80

B = 41

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The largest angle is adjacent to the largest side so

B C A

Step-by-step explanation:

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A fair spinner has 10 equal sections there is a probability scale

Answers

Answer:

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Step-by-step explanation:

Because there is ten different numbers so therefore it would be 10/1

Answer:

{1,2,4}

Step-by-step explanation:

Check image for more help

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What is the value 6^-8/6^-5?

Answers

Answer:

0.00462962962

Step-by-step explanation:

Good morning can anybody help me out with this assignment please and thanks! \
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Answers

Good Morning hope this helped.

Answer:

1: The cost of twelve bottles is $24 cause 12x2=24.

2: The ratio is 24/12 or 2/1

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The height in feet, h, of a base jumper Is jumping off a cliff is given by the equation
h = 3t^2 - 700t + 2000,
where t is the time is seconds. How long will it take the jumper to reach the ground?

Answers

Answer:

233 seconds

Step-by-step explanation:

When h = 0 the jumper ends his/her jump. Therefore let h = 0 so that we can solve for t; forming a quadratic equation

0 = 3t^2 - 700t + 200

I am going to solve  using the quadratic formula, but there are other approaches--

[tex]t_{1,\:2}=\frac{-\left(-700\right)\pm \sqrt{\left(-700\right)^2-4\cdot \:3\cdot \:200}}{2\cdot \:3},\\\\\sqrt{\left(-700\right)^2-4\cdot \:3\cdot \:200} = 20\sqrt{1219},\\\\t_{1,\:2}=\frac{-\left(-700\right)\pm \:20\sqrt{1219}}{2\cdot \:3}[/tex]

[tex]\:t_2=\frac{-\left(-700\right)-20\sqrt{1219}}{2\cdot \:3}[/tex]

[tex]t=\frac{10\left(35+\sqrt{1219}\right)}{3},\:t=\frac{10\left(35-\sqrt{1219}\right)}{3}[/tex]

Now the solutions are around 233 and 0.3 seconds. Given these two solutions I would find the first one more predictable.

QUICK! Should I wear a hoodie or a coat tomorrow?!!!

Answers

Answer:

HOODIEEE u a boy or girl?

Step-by-step explanation:

Hoodie tomorrow!!!!!!!!!!

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You add 3 to -6 and add 1 to 3 to get -3,4

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C

Step-by-step explanation:

Answer:

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Step-by-step explanation:


Write the equation of the line in point slope form.
(10 Points)

Answers

Answer:

y=-1/4(x-4)+3

Step-by-step explanation:

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Answers

Yep! Good job, you did it correctly.
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Riley earned $5 for 1 2 of an hour babysitting. What is her hourly rate? Simplify your answer and write it as a proper fraction, mixed number, or whole number.

Answers

Answer:

Riley's hourly rate is $10

Step-by-step explanation:

Riley earned $5 for 1/2 of an hour babysitting. What is her hourly rate?

1/2 of an hour = $5

1 hour = $x

Cross Multiply

1/2 × x = $5 × 1

x = $5 ÷ 1/2

x = $5 × 2

x = $10

Hence, Riley's hourly rate is $10

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Answer:

Step-by-step explanation:

(b+8)≤18

Solve for V in V = s^3, if 8 = 4 V =

Answers

Answer:

64 units³

Step-by-step explanation:

V =  S³

V =  4³

V = 64 Units³

3500 calories for 6 servings of pie ________ calories per serving is what?

Answers

Answer:

583 rounded to the nearest whole number

Step-by-step explanation:

other wise 583.3333333333333333333333333333

It would be 583 calories.

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Answers

Answer:

4^2+2^2, 5^2, 6^2-6

Step-by-step explanation:

4 to the power of 2 is 16 and 2 to the power of 2 is 4. 16+4 is 20.

5 to the power of 2 is 25 which is greater than 20.

6 to the power of 2 is 36 minus 6 is 30 which is greater than 25 and 20.

The graph of the quadratic function shown on the left is
y = –0.7(x + 3)(x – 4).

The roots, or zeros, of the function are
.



Determine the solutions to the related equation
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Answers

Answer: The roots are x = -3 and x = 4

Explanation:

We'll use the zero product property. This is the idea where if A*B = 0, then either A = 0 or B = 0.

So if

-0.7(x+3)(x-4) = 0

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Step-by-step explanation:

Substitution
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Answers

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Step-by-step explanation:

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For triangle ABC with A=103, B=24, a=16, find angle C

Answers

Answer:

given A=103° , B=24°

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Twice as many students are in the chess club as in the fencing club.The number of students in the fencing club is one fifth the number of students in the cooking club.There are 42 more students in the cooking club than in the chess club.How many students are in the chess club?

Answers

Answer:

28 students

Step-by-step explanation:

Let number of students in cooking club = x

Number of students in fencing club = 1/5 x

Number of students in chess club = 2(1/5)x

Since, There are 42 more students in the cooking club than in the chess club

Then ;

Number of students in chess club = Number of students in cooking club - 42

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10pts and I’ll mark brainliest!
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Answers

I think it is -5................

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Answers

Answer:

I have no idea

Step-by-step explanation:

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-3x2+27x-63=0

Answers

The answer is x= 23/9 or you can write it as x= 2 5/9 or x= 2.5

how do you find 20% plus 35%

Answers

Answer:

55%

Step-by-step explanation:

20% + 35% = 55%

I hope this helps!

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