What is the Definition of Math?

Answer:

The first three terms of the geometry sequence would be [tex]1[/tex], [tex]5[/tex], and [tex]25[/tex].

The sum of the first seven terms of the geometric sequence would be [tex]127[/tex].

Step-by-step explanation:

Let [tex]d[/tex] denote the common difference of the arithmetic sequence.

Let [tex]a_1[/tex] denote the first term of the arithmetic sequence. The expression for the [tex]n[/tex]th term of this sequence (where [tex]n\![/tex] is a positive whole number) would be [tex](a_1 + (n - 1)\, d)[/tex].

The question states that the first term of this arithmetic sequence is [tex]a_1 = 1[/tex]. Hence:

The common ratio of a geometric sequence is ratio between consecutive terms of that sequence. Let [tex]r[/tex] denote the ratio of the geometric sequence in this question.

Ratio between the second term and the first term of the geometric sequence:

[tex]\displaystyle r = \frac{1 + 2\, d}{1} = 1 + 2\, d[/tex].

Ratio between the third term and the second term of the geometric sequence:

[tex]\displaystyle r = \frac{1 + 12\, d}{1 + 2\, d}[/tex].

Both [tex](1 + 2\, d)[/tex] and [tex]\left(\displaystyle \frac{1 + 12\, d}{1 + 2\, d}\right)[/tex] are expressions for [tex]r[/tex], the common ratio of this geometric sequence. Hence, equate these two expressions and solve for [tex]d[/tex], the common difference of this arithmetic sequence.

[tex]\displaystyle 1 + 2\, d = \frac{1 + 12\, d}{1 + 2\, d}[/tex].

[tex](1 + 2\, d)^{2} = 1 + 12\, d[/tex].

[tex]d = 2[/tex].

Hence, the first term, the third term, and the thirteenth term of the arithmetic sequence would be [tex]1[/tex], [tex](1 + (3 - 1) \times 2) = 5[/tex], and [tex](1 + (13 - 1) \times 2) = 25[/tex], respectively.

These three terms ([tex]1[/tex], [tex]5[/tex], and [tex]25[/tex], respectively) would correspond to the first three terms of the geometric sequence. Hence, the common ratio of this geometric sequence would be [tex]r = 25 /5 = 5[/tex].

Let [tex]a_1[/tex] and [tex]r[/tex] denote the first term and the common ratio of a geometric sequence. The sum of the first [tex]n[/tex] terms would be:

[tex]\displaystyle \frac{a_1 \, \left(1 - r^{n}\right)}{1 - r}[/tex].

For the geometric sequence in this question, [tex]a_1 = 1[/tex] and [tex]r = 25 / 5 = 5[/tex].

Hence, the sum of the first [tex]n = 7[/tex] terms of this geometric sequence would be:

[tex]\begin{aligned} & \frac{a_1 \, \left(1 - r^{n}\right)}{1 - r}\\ &= \frac{1 \times \left(1 - 2^{7}\right)}{1 - 2} \\ &= \frac{(1 - 128)}{(-1)} = 127 \end{aligned}[/tex].

Answer:

Given the series,

∑ ∞ n = 1 − 4 ( − 1 / 2 ) n − 1

I think the series is summation from n = 1 to ∞ of -4(-1/2)^(n-1)

So,

∑ − 4 ( − ½ )^(n − 1). From n = 1 to ∞

There are different types of test to show if a series converges or diverges

So, using Ratio test

Lim n → ∞ (a_n+1 / a_n)

Lim n → ∞ (-4(-1/ 2)^(n+1-1) / -4(-1/2)^(n-1))

Lim n → ∞ ((-4(-1/2)^(n) / -4(-1/2)^(n-1))

Lim n → ∞ (-1/2)ⁿ / (-1/2)^(n-1)

Lim n→ ∞ (-1/2)^(n-n+1)

Lim n→ ∞ (-1/2)^1 = -1/2

Since the limit is less than 0, then, the series converge...

Sum to infinity

Using geometric progression formula

S∞ = a / 1 - r

Where

a is first term

r is common ratio

So, first term is

a_1 = -4(-½)^1-1 = -4(-½)^0 = -4 × 1

a_1 = -4

Common ratio r = a_2 / a_1

a_2 = 4(-½)^2-1 = -4(-½)^1 = -4 × -½ = 2

a_2 = 2

Then,

r = a_2 / a_1 = 2 / -4 = -½

S∞ = -4 / 1--½

S∞ = -4 / 1 + ½

S∞ = -4 / 3/2 = -4 × 2 / 3

S∞ = -8 / 3 = -2⅔

The sum to infinity is -2.67 or -2⅔

It looks like the series is

[tex]\displaystyle \sum_{n=1}^\infty \frac{n^{2n}}{(1+n)^{3n}} = \sum_{n=1}^\infty \left(\frac{n^2}{(1+n)^3}\right)^n[/tex]

Checking for convergence is most easily done with the (Cauchy) root test for convergence: the infinite series

[tex]\displaystyle \sum_{n=1}^\infty a_n[/tex]

converges absolutely if the limit

[tex]\displaystyle \lim_{n\to\infty} \sqrt[n]{|a_n|} < 1[/tex]

Here we have

[tex]\displaystyle \lim_{n\to\infty} \sqrt[n]{\left|\left(\frac{n^2}{(1+n)^3}\right)^n\right|} = \lim_{n\to\infty} \frac{n^2}{(1+n)^3} = 0 < 1[/tex]

so the given series converges.

Answer:

40,000

Step-by-step explanation:

Step-by-step explanation:

the value of x is 20 that's it good luck

Step-by-step explanation:

6c + c + 10 + c + 10 = 180

8c = 160

c = 20

Answer:

Perimeter

P = P1+P2

P1 = 4a           P2=2(a+b)

P1=4*5           P2=2(3+5)

P1=20            P2=2*8

                     P2=16

P = 20+16

P=36

Area

A=A1+A2

A1=[tex]a^{2}[/tex]                 A2=a*b

A1=[tex]5^{2}[/tex]                 A2=3*5

A1=25                A2=15

A=25+15

A=40

Answer:

3.43 seconds to do push ups and 2.66 seconds for him to do sit ups in the given time of 48 seconds ( to find the difference of time of each exercise done in the two different time, subtract each time unit from each other)

Step-by-step explanation:

for him to do 7 push ups and 15 sit ups in 66 seconds it would take time 4.71 second (5 seconds rounded) to do push ups. it would take him 2.20 seconds (2 seconds rounded) for him to do 15 sit ups in 66 seconds. for him to do it in 48 seconds, it would take him 3.43 (3 seconds rounded) to do 7 push ups in 48 seconds. for him to do 9 sit ups in 48 seconds it would take in 2.66 seconds ( 3 seconds rounded) for him to complete them in the given time.

Answer:

13

Step-by-step explanation:

it is on 100th place so 100th term is 13

Answer:

401

Step-by-step explanation:

arithmetic sequence formula: an=a1+d(n-1)

n= term # you're looking for

d= common difference

a1= 1st term in sequence

a100=5+4(100-1)

5+4(99)

5+396

a100=401

Answer:

25

Step-by-step explanation:

20 : 100 = 5 : x

x = (5 x 100) / 20 = 25

Answer:

[tex]\Large \boxed{\sf 384 \ m^2}[/tex]

Step-by-step explanation:

Surface area ⇒ area of 2 triangles + area of 3 rectangles

[tex](8 \times 3 \times 0.5 \times 2)+(20 \times 5 \times 2+20 \times 8)=384[/tex]

Answer:

Surface Area = 384 m²

Step-by-step explanation:

The given figure is a triangular prism.

The surface area of a triangular prism is made up of:

From inspection of the diagram, the dimensions of the triangular bases are:

[tex]\boxed{\begin{aligned}\textsf{Area of a triangle}&=\dfrac{1}{2} \times \sf base \times height\\\\\implies \textsf{Area of triangular base}&=\dfrac{1}{2} \times 8 \times 3\\&=4 \times 3\\&=12\; \sf m^2 \end{aligned}}[/tex]

From inspection of the diagram, there are two congruent rectangles with dimensions:

and one rectangle with dimensions:

[tex]\boxed{\begin{aligned}\textsf{Area of a rectangle}&=\sf width \times length\\\\\implies \textsf{Area of rectangle 1}&=5 \times 20\\&=100\; \sf m^2 \\\\\implies \textsf{Area of rectangle 2}&=8 \times 20\\&=160\; \sf m^2\end{aligned}}[/tex]

Therefore, the total surface area of the given triangular prism is:

[tex]\begin{aligned}\textsf{Total Surface Area}&=\sf 2\;Triangles + 2\;Rectangle\;1+Rectangle\;2\\& = 2 \times 12+ 2 \times100+160\\& = 24+200+160\\& = 224+160\\& = 384\; \sf m^2\\\end{aligned}[/tex]

Answer:dont lnow sorry. Only if u give me robux

Step-by-step explanation:

Answer: the answer for x is ( x = 2 (y+8)    a the

answer for y = x-16\2

Answer:

2 pies because you need 2 lb for each pie

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The answer is D, because when you divide x by a negative the sign changes

Answer:

B & D

Step-by-step explanation:

B & D

Answer:

Step-by-step explanation:

H0 : μ ≥ 6

H1 : μ < 6

Test statistic :

n = 20

Sample Mean, x = 3

σ = 1.5

Test statistic = (x - μ) ÷ σ/sqrt(n)

Test statistic = (3 - 6) ÷ 1.5/sqrt(20)

Test statistic = - 3 / 0.3354101

Test statistic = −8.944271

Since, sample size is < 30 ;

Obtaining the Critical value using the from T;

Tcritical at 0.05, df = 19 = - 1.729

Tstatistic < Tcritical

−8.944271 < - 1.729

Hence, we reject the Null:

We can conclude that there is significant evidence that the number of complaints received by Lara music store is different from number of complaints received by music stores in general.

Answer:

4

Hope it helps

Please mark me as the brainliest

Thank you

common difference = t2 - t1 for all terms.

therefore d = -2 - (-6)

= -2 + 6

= 4

hope it helps :D

Answer:

45 miles. 3*12 +3/4 *12 =x=>36+9=x=>x= 45.

Answer:

Answer:

Given data:

Put the data in the ascending order:

Mean, the average:

Median, average of middle two numbers:

Mode, the most repeated number:

Mean is normally the best measure of central tendency, same applies to this data.

Answer:

a=55

Step-by-step explanation:

20%/100=0.2

a=11/0.2

a=55

Answer:

sin θ/2 = ± √2/13

Step-by-step explanation:

tan θ = - 12/5       (in quadrant 4)      sin θ = - 12/13   and   cos θ = 5/13

sin θ/2 = ± (√1 - cos θ) / 2 = ± (√1 - 5/13) / 2 = ± √8/13 / 2 = ± √2/13

tan θ/2 = (1 - cos θ) / sin θ = sin θ / (1 + cos θ)

Let you to calculate the tan θ/2 part by yourself

Answer:

y=4

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation

x=2 is where you could fold the quadratic function and have the sides overlap perfectly

Answer:

Hi yes ik I'm not that good at math but wouldn't it be

a n=1∗1 n =1

Answer:

2.75632 rounded to 5 decimal places

Step-by-step explanation:

a(r^n-1)/r-1 is the formula for sum of geometric series

where a= first term (1.4)

n= number of terms(6)

r= common ratio(0.5)