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Aneli [31]
3 years ago
9

What is the explicit formula for the arithmetic sequence?

Mathematics
2 answers:
soldier1979 [14.2K]3 years ago
8 0
Mathwords: Arithmetic Sequence. A sequence such as 1, 5, 9, 13, 17 or 12, 7, 2, –3, –8, –13, –18 which has a constant difference between terms. The first term is a1, the common difference is d, and the number of terms is n.
Svetradugi [14.3K]3 years ago
3 0

Answer with explanation:

To obtain the nth term of a Sequence we derive Explicit formula.

For, Arithmetic Sequence

A sequence in which difference between two consecutive terms is same, that is , A sequence

  a_{1},a_{2},a_{3},.................a_{n},\text{Such that}\\\\a_{2}-a_{1}=a_{3}-a_{2}=.....a_{n}-a_{n-1}=d,

is an Arithmetic Sequence.

To Derive the Explicit Formula ,The following sequence can be written as:

a_{1}=a\\\\a_{2}=a+(2-1)d=a+d\\\\a_{3}=a+(3-1)d=a+2 d\\\\a_{4}=a+(4-1)d=a+3 d\\\\a_{5}=a+(5-1)d=a+4 d\\\\a_{6}=a+(6-1)d=a+5 d\\\\a_{7}=a+(7-1)d=a+6 d

......................................

........................................

a_{n}=a+(n-1)d

This is Required explicit formula for the arithmetic sequence.

   

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Write a problem that can be solved using the equation:9x+14=100
Keith_Richards [23]

The correct answer is Option C. Ty saved $14 and he earns $9 each week. How many weeks will it take till he has $100?

Further explanation:

Given equation is:

9x+14

We will look at the options one by one

<u>A.9 dogs and 14 dogs and 14 cats cost $100</u>

If this option has to be considered, there will be atleast two variables involved one for the dogs and one for the cats while the given equation only involves one variable so this is not the correct option.

<u>B. Ty wants to buy 14 dogs, but they cost $100, how much more does he need?</u>

The given scenario cannot be linked to given equation if x represents dogs the equation will be something like 14x=100 so this option is not the correct answer.

<u>C. Ty saved $14 and he earns $9 each week. How many weeks will it take till he has $100?</u>

The number 14 will be constant as this is the value which is used only once while ty earns 9 dollar per week if x represents number of weeks then the equation to represent the scenario will be

9x+14=100

The value of x will give us the number of weeks required.

The correct answer is Option C. Ty saved $14 and he earns $9 each week. How many weeks will it take till he has $100?

Keywords: Linear equations, linear inequality

Learn more about linear equations at:

  • brainly.com/question/1517035
  • brainly.com/question/1506379

#LearnwithBrainly

5 0
3 years ago
How do I simplify (2x1/4) -4th power?
alina1380 [7]
Since the 2 and x^1/4 are multiplying we can do the math separately and then just multiply them afterwards

2^-4 is the same as 1/(2^4) which is 1/16

(x^1/4)^-4    (POWER RULES REVIEW)
                          2 exponents of same base you just add (basically multiply                                                                                                              the two)
so x^(1/4x-4)  = x^(-1)

which is just 1/x

so the answer is 1/16x
 
5 0
3 years ago
imagine that the number 2 button on your calculator is damaged and cannot be used.use a flow chart to show 3 different ways in w
jeka94
(6x4)(4x3)
Hope this helps you. I accidentally wrote my answer in the comment box.
8 0
3 years ago
Two diagonals divide a square into 4 congruent triangles. The base of each triangle is 8 inches and the height is 5 inches. What
madam [21]

Answer:

64

Step-by-step explanation:

Youd do 8x8 because the base of the triangles are 8 and a square has equal sides all around

3 0
3 years ago
Hyperbolas
Olenka [21]

let's notice something on this hyperbola, the fraction that is positive, is the fraction with the "y" variable, that simply means that the hyperbola is opening vertically, namely runs over the y-axis or it has a vertical traverse axis, which means, that, the foci will be a certain "c" distance from the center over the y-axis, well, with that mouthful, let's proceed.

\bf \textit{hyperbolas, vertical traverse axis } \\\\ \cfrac{(y- k)^2}{ a^2}-\cfrac{(x- h)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h, k\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2}\\ asymptotes\quad y= k\pm \cfrac{a}{b}(x- h) \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}

\cfrac{(y-3)^2}{1}-\cfrac{(x+2)^2}{4}=1\implies \cfrac{[y-3]^2}{1^2}-\cfrac{[x-(-2)]^2}{2^2}=1~~ \begin{cases} h=-2\\ k=3\\ a=1\\ b=2 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ c=\sqrt{a^2+b^2}\implies c=\sqrt{1+4}\implies c=\sqrt{5} \\\\\\ \stackrel{\textit{so then the foci are at}}{(-2~~,~~3\pm \sqrt{5})}\qquad \qquad \qquad \stackrel{\textit{and its vertices are at }}{(-2~~,~~3\pm 1)}\implies \begin{cases} (-2,4)\\ (-2,2) \end{cases}

now let's check for the asymptotes.

\bf y=3\pm \cfrac{1}{2}[x-(-2)]\implies y=3\pm \cfrac{1}{2}(x+2) \\\\[-0.35em] ~\dotfill\\\\ y=3+ \cfrac{1}{2}(x+2)\implies y=3+\cfrac{x+2}{2}\implies y=\cfrac{6+x+2}{2} \\\\\\ y=\cfrac{x+8}{2}\implies y=\cfrac{1}{2}x+4 \\\\[-0.35em] ~\dotfill\\\\ y=3- \cfrac{1}{2}(x+2)\implies y=3-\cfrac{(x+2)}{2}\implies y=\cfrac{6-(x+2)}{2} \\\\\\ y=\cfrac{6-x-2}{2}\implies y=\cfrac{-x+4}{2}\implies y=-\cfrac{1}{2}x+2

8 0
3 years ago
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