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2 years ago

2. The algebraic form of an arithmetic sequence is 4 n+1.

Mathematics

2 answers:

erma4kov [3.2K]2 years ago

5 0

Answer:

Given:-

The algebraic form of an arithmetic sequence is 4n+1.

To find:-

common difference.

first term

remainder when each term of the sequence is divided by 4.

Solution:-

Given,

and n = 1,2,3...

Now,

If n = 2,

The sequence is 5 ,9,13..

Hence, the first term is 5.

Common difference :

=> d =

=> 9- 5

=> d = 4.

Hence, common difference is 4.

Remainder :

=> 5/4 = 4(4) +1

Here, remainder =1

=> 9/4 = 4(2)+1

Here, remainder =1

=> 13/4 = 4 (3)+1

Here , remainder = 1.

Therefore, the remainder when each term of this sequence is divided by 4 is 1 .

Step-by-step explanation:

baherus [9]2 years ago

4 0

Answer:

Below in bold.

Step-by-step explanation:

The nth term = a + d(n - 1) where a = first term and d = common difference

= dn + a - d

So comparing this to 4n + 1:

a) d = 4

b) a - d = a - 4 = 1

so a first term = 5.

c) (4n + 1) / 4 = n remainder 1

The remainder is 1.

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melamori03 [73]

Answer:

51/4

Step-by-step explanation:

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X~ Uniform(0,100)

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$f(x) = P(X=x) = 1/100 \,\,\,\, \text{if} \,\,\,\, 0 \leq x \leq 100\\f(x) = P(X=x) = 0 \,\,\,\, \text{otherwise}$

Now, imagine that the D represents the distance from the break down point to the nearest station. Think about this, the first service station is 20 meters away from city A, and the second station is located 70 meters away from city A then the mid point between 20 and 70 is (70+20)/2 = 45 then we can represent D as follows

$D(x) =\left\{ \begin{array}{ll} x & \mbox{if } 0\leq x \leq 20 \\ x-20 & \mbox{if } 20\leq x < 45\\ 70-x & \mbox{if } 45 \leq x \leq 70\\ x-70 & \mbox{if } 70 \leq x \leq 100\\ \end{array}\right.$

Now, as we said before X represents the random variable where the bus breaks down, then we form a new random variable $Y = D(X)$ , $Y$ is a random variable as well, remember that there is a theorem that says that

$E[Y] = E[D(X)] = \int\limits_{-\infty}^{\infty} D(x) f(x) \,\, dx$

Where $f(x)$ is the probability mass function of X. Using the information of our problem

$E[Y] = \int\limits_{-\infty}^{\infty} D(x)f(x) dx \\= \frac{1}{100} \bigg[ \int\limits_{0}^{20} x dx +\int\limits_{20}^{45} (x-20) dx +\int\limits_{45}^{70} (70-x) dx +\int\limits_{70}^{100} (x-70) dx \bigg]\\= \frac{51}{4} = 12.75$

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Delicious77 [7]

Answer:

Step-by-step explanation:

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$4p(x-h)=(y-k)^2$

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3 years ago

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harina [27]

Answer:

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Step-by-step explanation:

The grand topic is MATRICES.

In Matrices, there are rules to follow when creating a matrix - which is a 'row by column' arrangement of objects or figures.

Rule 1: Identify your rows and columns.

What is a row? A row is a 'left to right' arrangement of items; also called a horizontal arrangement of items. What is a column? A column is an 'up to down' arrangement of items; also called a vertical arrangement of items.

Rule 2: Start your arrangement by rows.

Before reaching the instruction in the question, I already arranged the data for cables on the rows and the data for wire colors on the columns. You should follow this rule always; from the first information given in the question.

Rule 3: Nomenclature

This is the naming of a given matrix. In naming a matrix, consider the rows first before the columns. For example, a matrix with three rows and four columns with be called a 3 by 4 matrix and not a 4 by 3 matrix. In the case of this question, there is an equal number of rows and columns, so even if you counted the columns first, it wouldn't be noticed. Nevertheless, always count the rows first.

Having arranged the figures in a 3 by 3 matrix,

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So the answer is $\left[\begin{array}{ccc}3&3&2\\1&2&1\\2&1&2\end{array}\right]$

Kudos!

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3 years ago