Help me solve this equation. (x-5) =10 where y =3

Solve the following recurrence relation: <img src="https://tex.z-dn.net/?f=A_%7Bn%7D%3Da_%7Bn-1%7D%2Bn%3B%20a_%7B1%7D%20%3D

-Dominant- [34]

By iteratively substituting, we have

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

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

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

and the pattern continues down to the first term $a_1=0$ ,

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

$\implies a_n = a_1 + \displaystyle \sum_{k=0}^{n-2} (n - k)$

$\implies a_n = \displaystyle n \sum_{k=0}^{n-2} 1 - \sum_{k=0}^{n-2} k$

Recall the formulas

$\displaystyle \sum_{n=1}^N 1 = N$

$\displaystyle \sum_{n=1}^N n = \frac{N(N+1)}2$

It follows that

$a_n = n (n - 2) - \dfrac{(n-2)(n-1)}2$

$\implies a_n = \dfrac12 n^2 + \dfrac12 n - 1$

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

4 0

2 years ago

A right rectangular prism has base dimensions of 3 inches by 12 inches and a height of 5 inches. An oblique rectangular prism ha

Deffense [45]

The volumes will be the same, because the heights are equal and the cross-sectional areas at every level parallel to the bases are also equal.

6 0

2 years ago

Read 2 more answers

Which expression is equivalent to the square root of 2 multipllied by 5 divided by 18

gayaneshka [121]

Answer:.75

Step-by-step explanation:

2x5/18 =.55555

.556 root is .745 the five makes the 4 round up

5 0

3 years ago

You select a letter at random from the letters shown. Express the following probabilities as a fraction, a decimal, and a percen

docker41 [41]

Answer:

B

Step-by-step explanation:

ou select a letter at random from the letters shown. Express the following probabilities as a fraction, a decimal, and a percent. letters A B C D E

A) P (vowel)

B) P (consonant)

7 0

3 years ago

Read 2 more answers

When finding the sum of 512 and –614, Josh used a left-to-right algorithm to compute the answer. He first added the hundred’s di

Georgia [21]

Answer:

Yes, Josh's answer is correct as  –102 is the correct answer.

Josh have computed the sum as:

If the two integers having different signs, we need to subtract the absolute values (the digits without signs) and then just make sure to keep the sign of the number with the larger absolute value.

− 6 1 4

+ + 5 1 2

_________

- 1 0 2

_________

Staring from right, − 614 + (+512) = -102 can be obtained by first adding 2 in negative 4, then adding 1 in negative 1, and lastly adding 5 in negative 6.

Ultimately we can say that Negative 614 plus Positive 514 equals Negative 102.

So, the sum of 512 and –614 is -102 i.e − 614 + (+512) = -102

Step-by-step explanation:

This is how Josh used a left-to-right algorithm to compute the answer:

Adding the hundred’s digits 500 + (–600) = –100
Adding the ten's digits 10 + (–10) = 0
Lastly, adding 2 + (–4) = –2
End result –100 + 0 + (–2) = –102

Yes, Josh's answer is correct. 

How else could Josh have computed the sum?

Before mentioning how Josh could have computed the sum. Here are some of the facts about sum of numbers:

The sum of two negative integers is a negative integer. For example,

Adding two negative integers: -3 and -5

-3 + -5 = -8

Please, you don't need to confuse the sign or symbol of the integer with the operation being performed.

Just note -3 + -5 = -8 which is read as is read as Negative 3 plus negative 5 equals negative 8.

The sum of two positive integers is a positive integer.

Adding two positive integers: ⁺3 and ⁺5

(⁺3) + (⁺5) = ⁺8

Please, you don't need to confuse the sign or symbol of the integer with the operation being performed.

Just note ⁺3 + ⁺5 = ⁺8 which is read as is read as Positive 3 plus positive 5 equals positive 8.

To add a positive and a negative integer

As +(+) are like signs, so they become a positive sign. Such as:

−5 + (+ 1) = −5 + 1 = -4

As

+ + ⇒ +

+ − ⇒ −

− + ⇒ −

− − ⇒ +

If the two integers having different signs, we need to subtract the absolute values (the digits without signs) and then just make sure to keep the sign of the number with the larger absolute value.

So, What is −614 + (+512)?

− 6 1 4

+ + 5 1 2

_________

- 1 0 2

_________

Staring from right, − 614 + (+512) = -102 can be obtained by first adding 2 in negative 4, then adding 1 in negative 1, and lastly adding 5 in negative 6.

Ultimately we can say that Negative 614 plus Positive 514 equals Negative 102.

So, the sum of 512 and –614 is -102 i.e − 614 + (+512) = -102

Keywords: integer, sum, numbers, digit

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3 0

3 years ago