Which of these represents an integer?<br> a. -3 b. 4 c. 2 1/2 d. 6.2

Write an expression to match the statement 1/5 of the difference between 18 and 11

Artemon [7]

$(18 - 11) \div 5$

8 0

4 years ago

Read 2 more answers

Determine formula of the nth term 2, 6, 12 20 30,42

nalin [4]

Check the forward differences of the sequence.

If $\{a_n\} = \{2,6,12,20,30,42,\ldots\}$ , then let $\{b_n\}$ be the sequence of first-order differences of $\{a_n\}$ . That is, for n ≥ 1,

$b_n = a_{n+1} - a_n$

so that $\{b_n\} = \{4, 6, 8, 10, 12, \ldots\}$ .

Let $\{c_n\}$ be the sequence of differences of $\{b_n\}$ ,

$c_n = b_{n+1} - b_n$

and we see that this is a constant sequence, $\{c_n\} = \{2, 2, 2, 2, \ldots\}$ . In other words, $\{b_n\}$ is an arithmetic sequence with common difference between terms of 2. That is,

$2 = b_{n+1} - b_n \implies b_{n+1} = b_n + 2$

and we can solve for $b_n$ in terms of $b_1=4$ :

$b_{n+1} = b_n + 2$

$b_{n+1} = (b_{n-1}+2) + 2 = b_{n-1} + 2\times2$

$b_{n+1} = (b_{n-2}+2) + 2\times2 = b_{n-2} + 3\times2$

and so on down to

$b_{n+1} = b_1 + 2n \implies b_{n+1} = 2n + 4 \implies b_n = 2(n-1)+4 = 2(n + 1)$

We solve for $a_n$ in the same way.

$2(n+1) = a_{n+1} - a_n \implies a_{n+1} = a_n + 2(n + 1)$

Then

$a_{n+1} = (a_{n-1} + 2n) + 2(n+1) \\ ~~~~~~~= a_{n-1} + 2 ((n+1) + n)$

$a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))$

$a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))$

and so on down to

$a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2$

$\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}$

6 0

2 years ago

Please help me please!!!!!

EastWind [94]

A^2 + b^2 = c^2
( use Pythagorean theorem)
8^2+17^2=c^2

5 0

4 years ago

Select the correct answer.

Marat540 [252]

The correct answer is option C the error is that the linear pair of the theorem can not be used to say that ∠AOP is complementary to ∠POB

<h3>What is the Linear pair theorem?</h3>

The linear pair postulate or linear pair theorem in mathematics states the same thing mathematically. The sum of the measurements of two angles that make up a linear pair is 180°.

In the proof of the given question, it is given that the ∠AOP and ∠POB are complementary angles by linear pair of theorem but the linear pair of the theorem is applied to the angles with the sum of 180.

Therefore the correct answer is option C the error is that the linear pair of the theorem can not be used to say that ∠AOP is complementary to ∠POB

To know more about the Linear pair theorem follow

brainly.com/question/5598970

#SPJ1

6 0

3 years ago

Someone help me who is good in math. Please HELP!!!!

larisa [96]

If AC bisects BD, then BC = CD

That means:

2y - 2 = y + 3

Solve:

y -2 = 3

y = 5

3 0

3 years ago

Read 2 more answers

Which of these represents an integer? a. -3 b. 4 c. 2 1/2 d. 6.2