Please answer this math problem... I will mark you brainliest

Geometric sequence is characterized by a common ratio

(1) Sum of first 5 terms

The first term of the sequence is:

[tex]\mathbf{a = 3}[/tex]

The common ratio (r) is:

[tex]\mathbf{r = 6 \div 3 = 2}[/tex]

The sum of n terms is calculated using:

[tex]\mathbf{S_n = \frac{a(r^n - 1)}{r - 1}}[/tex]

So, we have:

[tex]\mathbf{S_5 = \frac{3 \times (2^5 - 1)}{2 - 1}}[/tex]

[tex]\mathbf{S_5 = \frac{93}{1}}[/tex]

[tex]\mathbf{S_5 = 93}[/tex]

Hence, the sum of the first five terms is 93

(2) Sum of first 5 terms

The first term of the sequence is:

[tex]\mathbf{a = 14}[/tex]

The common ratio (r) is:

[tex]\mathbf{r = 3}[/tex]

The sum of n terms is calculated using:

[tex]\mathbf{S_n = \frac{a(r^n - 1)}{r - 1}}[/tex]

So, we have:

[tex]\mathbf{S_5 = \frac{14 \times (3^5 - 1)}{3 - 1}}[/tex]

[tex]\mathbf{S_5 = \frac{3388}{2}}[/tex]

[tex]\mathbf{S_5 = 1694}[/tex]

Hence, the sum of the first five terms is 1694

(3) Sum of first n terms

The first term of the sequence is:

[tex]\mathbf{a = 318}[/tex]

The common ratio (r) is:

[tex]\mathbf{r = \frac12}[/tex]

The sum of n terms is calculated using:

[tex]\mathbf{S_n = \frac{a(1 - r^n)}{1 - r}}[/tex]

So, we have:

[tex]\mathbf{S_n = \frac{318 \times (1 - \frac 12^n)}{1 - \frac 12}}[/tex]

[tex]\mathbf{S_n = \frac{318 \times (1 - \frac 12^n)}{\frac 12}}[/tex]

[tex]\mathbf{S_n = 636 (1 - \frac 12^n)}[/tex]

Hence, the sum of the first n terms is [tex]\mathbf{ 636 (1 - \frac 12^n)}[/tex]

(4) The first term

The sum of the first 7th term of the sequence is:

[tex]\mathbf{S_7 = 547}[/tex]

The common ratio (r) is:

[tex]\mathbf{r = -3}[/tex]

The sum of n terms is calculated using:

[tex]\mathbf{S_n = \frac{a(1 - r^n)}{1 - r}}[/tex]

So, we have:

[tex]\mathbf{547 = \frac{a(1 - (-3)^7)}{1 - -3}}[/tex]

[tex]\mathbf{547 = \frac{a(2188)}{4}}[/tex]

Multiply both sides by 4

[tex]\mathbf{2188= a(2188)}[/tex]

Divide both sides by 2188

[tex]\mathbf{1= a}[/tex]

Rewrite as:

[tex]\mathbf{a = 1}[/tex]

Hence, the first term is 1

(5) Find the 7th term

The first term of the sequence is:

[tex]\mathbf{a=2}[/tex]

The common ratio (r) is:

[tex]\mathbf{r=3}[/tex]

The nth term of a geometric sequence is:

[tex]\mathbf{T_n = ar^{n -1}}[/tex]

So, we have:

[tex]\mathbf{T_7 = 2 \times 3^{7 -1}}[/tex]

[tex]\mathbf{T_7 = 1458}[/tex]

Hence, the seventh term is 1458

(6) Sum of geometric sequence

The first term of the sequence is:

[tex]\mathbf{a=2}[/tex]

The common ratio of the sequence is:

[tex]\mathbf{r = 6 \div 2 = 3}[/tex]

The number of terms is:

[tex]\mathbf{n = 5}[/tex]

The sum of n terms is calculated using:

[tex]\mathbf{S_n = \frac{a(r^n - 1)}{r - 1}}[/tex]

So, we have:

[tex]\mathbf{S_5 = \frac{2 \times (3^5 - 1)}{3 - 1}}[/tex]

[tex]\mathbf{S_5 = \frac{484}{2}}[/tex]

[tex]\mathbf{S_5 = 242}[/tex]

Hence, the sum of the first five terms is 242

(7) The first term

The sum of the first five terms is given as:

[tex]\mathbf{S_5 = 341}[/tex]

The common ratio is:

[tex]\mathbf{r = 4}[/tex]

The sum of n terms is calculated using:

[tex]\mathbf{S_n = \frac{a(r^n - 1)}{r - 1}}[/tex]

So, we have:

[tex]\mathbf{341 = \frac{a \times (4^5 - 1)}{4 - 1}}[/tex]

[tex]\mathbf{341 = \frac{a \times 1023}{3}}[/tex]

Solve for a

[tex]\mathbf{a = \frac{3 \times 341}{1023}}[/tex]

[tex]\mathbf{a = 1}[/tex]

Hence, the first terms is 1

(8) Sum to infinite

The first term of the sequence is:

[tex]\mathbf{a = 192}[/tex]

The common ratio (r) is:

[tex]\mathbf{r = \frac 14}[/tex]

The sum to infinite is:

[tex]\mathbf{S_{\infty} = \frac{a}{1 - r}}[/tex]

So, we have:

[tex]\mathbf{S_{\infty} = \frac{192}{1 - 1/4}}[/tex]

[tex]\mathbf{S_{\infty} = \frac{192}{3/4}}[/tex]

[tex]\mathbf{S_{\infty} = 256}[/tex]

Hence, the sum to infinite is 256

Read more about geometric sequence at:

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Answer:

135

Step-by-step explanation:

720 degrees in a 6 sided shape. already have 2 right angles so its 720- 180 = 540

540÷4 is 135

Answer:

Use the coordinate plane below to answer the following questions. a. Use a straightedge to construct a line that goes.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Bbdbbdbs

Answer:

£9184

Step-by-step explanation:

Interest = PRT/100

P = Price

R = Rate

T = time

First Let's find the interest for 2 years

[tex]interest = \frac{8200 \times 6 \times 2}{100} \\ = 984[/tex]

So, the interest is £984

Now let's find the full amount he received after two years ,

[tex]8200 + 984 = 9184[/tex]

Total Amount = £9184

Hope this helps you

Let me know if you have any other questions :-):-)

Step-by-step explanation:

0.075 % is the probability of that

Answer:

40 ounces

Step-by-step explanation:

Answer:

it is not balanced because of sulphur on left side 2 sulphur

on the right side 3 sulphur

Answer:

the equation is - [tex]y=x[/tex]

Explanation:

Given -

[tex]y=x+4[/tex]

We have to find a line passing through the point [tex](2,2)[/tex] nd parallel to the given line.

Find the slope of the given line.

It is the coefficeint of [tex]x[/tex]

m₁ = 1

The two lines are parallel. Hence

m₂=m₁=1 Where m₂is the slope of the second line.

You have slope and the points [tex](2,2)[/tex]

Find the Y intercept

[tex]y=mx+c\\2=(1)(2)+C\\2=2+C\\C=2-2=0[/tex]

Y-Intercept [tex]C=0[/tex] and slope m₂=1

Fix the equation

[tex]y=x[/tex]

Answer:

3

Step-by-step explanation:

3 is the only number here with factors of itself (3) and 1

Answer:

3

Step-by-step explanation:

7+(-3x)

7+(-36)

-29

I hope this helps!

Answer:

Direction: Opens Up

Vertex: ( 5 , − 25 )

Axis of Symmetry: x = 5

I'm not sure if this was a graphing question however that is how you solve it.

Answer:

14

Step-by-step explanation:

Answer:

[tex]find \: f(0) \\ \\ f(x) = - x + 2 \\ f(0) = - (0) + 2 \\ f(0) = - 0 + 2 \\ f(0) = 2[/tex]

Step-by-step explanation:

write this equation on a pice of paper then go to the camera button select which one you want and then take a pic of it. i am in a math class a year above me and this is what we are learning these types of problems confuse me I wish I could help

Answer: 2400

Step-by-step explanation:

120*20

The  power consumed by circuit is 2400 watt

The quantity of energy transferred or transformed per unit of time is known as power. The watt, or one joule per second, is the unit of power in the International System of Units.

Electrical power is the product of voltage and current. P = V X I .

Given:

Potential Difference= 120 vatt

Current = 20 Ampere

Now, using

Power = V x I

Power= 120 x 20

Power = 2400 Watt

Hence, the power consumed by circuit is 2400 watt

Learn more about power here:

https://brainly.com/question/22103646

#SPJ5

The 1/4x is the slope and +2 is (2,0).

Answer:  

y = 4x² -19x -5

Step-by-step explanation:  

When you graph it (or use an appropriate tool), it can help us to figure out that the equation is:

y = 4x² -19x -5

(Quadratic regression = the process of determining the equation of a parabola that best fits a set of data)

Hope this helps, have a nice day :D

Answer:

y=-2x^2+14x+(-7)

Step-by-step explanation:

using the 3 points of (-1, -23) (-3, -67) (2, 13)

Answer:

24.5

Step-by-step explanation:

24.5 is the temperature change each hour

9514 1404 393

Answer:

  172 : 227

Step-by-step explanation:

The ratio can be turned to an integer ratio by multiplying both values by 2.

  86 : 113.5= 2·86 : 2·113.5 = 172 : 227

Answer:

You returned 5 shirt.

Step-by-step explanation:

$30.60 ÷ $6.12 = 5

Answer:

5 shirts

Equation:

-$30.60 / -$6.12 = 5

So 5 would be your answer! :)

Answer:

week 4 each will have $31

Step-by-step explanation:

Answer:

Week 4

Step-by-step explanation:

Bob's savings over the course of 4 weeks

15 + 4 = 19(W1) + 4 = 23(W2) + 4 = 27(W3) + 4 = 31(W4)

John's savings over the course of 4 weeks

3 + 7 = 10(W1) + 7 = 17(W2) + 7 = 24(W3) + 7 = 31 (W4)

Answer:

Answer :- Statement (B) ,C'D' ll AB

Given AB is parallel to CD.  CD rotated.

Consider a transversal line l intersecting AB and CD at angle x.

therefore By slope formula,

slope of AB and CD = m =tanx

Now after rotation of 180 CD become C'D'

therefore, slope of C'D' = =tanx=m

Hence C'D' ll AB.

Answer:

(-4,0)

Step-by-step explanation:

1. First, let's graph f(x) = |x + 4|.

(The image is below the explanation).

2. As you can see, the line at first starts going down, but then the turning point occurs at (-4,0). The graph then continues to go upwards.

Therefore, the answer is (-4, 0).