All categories

3 years ago

Use sigma notation to represent the sum of the first seven terms of the following sequence: 4, 10, 16, … the summation from n eq

uals 1 to 7 of negative 4 plus 6 times n the summation from n equals 1 to 7 of 4 plus 6 times n the summation from n equals 1 to 7 of 2 plus 6 times n the summation from n equals 1 to 7 of negative 2 plus 6 times n

Mathematics

1 answer:

Dominik [7]3 years ago

6 0

$\bf 4~~,~~\stackrel{4+6}{10}~~,~~\stackrel{10+6}{16}~~,~~...~\hspace{10em}\stackrel{\textit{common difference}}{d = 6} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=4\\ d = 6 \end{cases} \implies a_n=4+(n-1)6 \\\\\\ a_n=4-6+6n\implies a_n=6n-2~\hfill \displaystyle\boxed{\sum\limits_{n = 1}^{7}~6n-2}$

You might be interested in

Jorge randomly selects a digit from 0 to 9. What is the probability that the digit he selects is a prime number?

zloy xaker [14]

Step-by-step explanation:

{0,1,2,3,4,5,6,7,8,9}--set of numbers from 0 to 9

{2,3,5,7}---set of prime numbers from 0 tp 9

there are 10 numbers in the first set and 4 numbers in the second set.

4/9 is the probability that the digit he selects is a prime number

Hope that helps :)

3 0

3 years ago

The graph of an absolute value function has a vertex of (2,3) and crosses the x-axis at (−1,0) and (5,0). What is the equation f

frez [133]

Answer:

Option D.

Step-by-step explanation:

The vertex form of an absolute function is

$y=a|x-h|+k$

where, a is a constant, (h,k) is vertex.

It is given that, vertex of an absolute function is (2,3). So, h=2 and k=3.

$y=a|x-2|+3$ ...(1)

It crosses the x-axis at (5,0). So put x=5 and y=0 to find the value of a.

$0=a|5-2|+3$

$-3=3a$

$-1=a$

Put a=-1 in (1).

$y=(-1)|x-2|+3$

$y=-|x-2|+3$

Now, put y=0, to find the equation for this absolute value function when y=0.

$0=-|x-2|+3$

Therefore, the correct option is D.

4 0

4 years ago

Read 2 more answers

Which of the following is a solution to 2cos2x − cos x − 1 = 0?

Pavel [41]

Answer:

Option A is correct.

Solution for the given equation is, $x = 0^{\circ}$

Step-by-step explanation:

Given that : $2\cos^2x -\cos x -1 =0$

Let $\cos x =y$

then our equation become;

$2y^2-y-1= 0$ .....[1]

A quadratic equation is of the form:

$ax^2+bx+c =0$ .....[2] where a, b and c are coefficient and the solution is given by;

$x = \frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Comparing equation [1] and [2] we get;

a = 2 b = -1 and c =-1

then;

$y = \frac{-(-1)\pm \sqrt{(-1)^2-4(2)(-1)}}{2(2)}$

Simplify:

$y = \frac{ 1 \pm \sqrt{1+8}}{4}$

$y = \frac{ 1 \pm \sqrt{9}}{4}$

$y = \frac{ 1 \pm 3}{4}$

$y = \frac{1+3}{4}$ and $y = \frac{1 -3}{4}$

Simplify:

y = 1 and $y = -\frac{1}{2}$

Substitute y = cos x we have;

$\cos x = 1$

⇒ $x = 0^{\circ}$

and

$\cos x = -\frac{1}{2}$

⇒ $x = 120^{\circ} \text{and} x = 240^{\circ}$

The solution set: $\{0^{\circ}, 120^{\circ} , 240^{\circ}\}$

Therefore, the solution for the given equation $2\cos^2x -\cos x -1 =0$ is, $0^{\circ}$

8 0

4 years ago

Read 2 more answers

Someone answer this please!!

Ronch [10]

B would be correct. The first two people, out of 100, would have painted 42.5/100 of the building.

7 0

3 years ago

What is 0.467 + 0.025?<br> O A. 0.442<br> B. 0.4695<br> C. 0.492<br> OD. 0.717

enyata [817]

Answer:

C. 0.492

Step-by-step explanation:

All I did was add the two numbers. Add them like normal, even though they are in decimal form. You could also use a calculator. If you don't have one, there should be one programed into your phone and computer.

0.467

+ 0.025

= 0.492

I hope this helps! Please let me know if you have any more questions or need any more help. Have a great day!

5 0

3 years ago