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4 years ago

An arithmetic sequence has this recursive formula: What is the explicit formula for this sequence? A. an = (–1) + (n – 7)(–4)

Mathematics

2 answers:

Rainbow [258]4 years ago

6 0

Answer:

The explicit formula of the given sequence

$a_n=27-4n$

Step-by-step explanation:

Given A sequence is in an arthmetic progression

The recursive formula

$a_n=(-1)+(n-7)(-4)$

Recursive formula:It is the formula to find the value of $n^{th}$ term ( $a_n$ ) of the sequence when $(n-1)^{th}$ term of the sequence is known .

Explicit formula:It is the formula to find the value of any term of the sequence when $n^{th}$ term is known.

$a_n= -1-4n+28$

By simplification

$a_n= 27-4n$

By simplification

Hence, the explicit formula , $a_n=27-4n$ .

tresset_1 [31]4 years ago

4 0

bearing in mind that an explicit form is simply the sequence written as a function of some variables, so we simply simplify and add like-terms.

$\bf a_n=(-1)+(n-7)(-4)\implies a_n=-1+(-4n+28)\implies a_n=27-4n$

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According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? f(x) = 8x7 – x5 + x3+6

valentina_108 [34]

According to the Fundamental Theorem of Algebra, the number of roots of a polynomial is equal to the degree of the polynomial. The degree of the polynomial is the highest exponent of a term in the polynomial.
Looking at the function, the term with the highest exponent is 8x7. The exponent is 7; therefore, the function has 7 roots.

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3 years ago

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Ahmed received a box of gifts. The box is a rectangular prism with the same height and width, and the length

liubo4ka [24]

Answer:

12 inches

Step-by-step explanation:

Ahmed received a box of gifts. The box is a rectangular prism with the same height and width, and the length

is twice the width. The volume of the box is 3,456 in? What is the height of the box?

Volume of a Rectangular pyramid = Length × Width × Height

From the above question

Height = Width = x

Length = 2 × Width

Length = 2x

Volume = 3,456 cubic inches

Hence,

3,456 = 2x × x × x

3456 = 2x³

x³ = 3456/2

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Cube root both sides

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x = 12 inches

Therefore, the height is 12 inches

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3 years ago

If you had to add two fractions with denominators of 4 and 5. What might the denominator of the sum be? Show more than one possi

mylen [45]

Answer:

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3 years ago

Factor the polynomial function over the complex numbers. f(x)=x^4-x^3-2x−4 Enter your answer in the box. f(x) = The answer is: (

Vladimir79 [104]

Answer:

Factors: $(x+i\sqrt2)(x-i\sqrt2)(x+1)(x-2)=0$

Step-by-step explanation:

We are given a polynomial:

$f(x)=x^4-x^3-2x-4$

We have to factor the given polynomial into its complex factors.

The factorization can be done as follows:

$f(x)=x^4-x^3-2x-4 = 0\\x^4-x^3-2x-4 = 0\\x^4-4-x^3-2x=0\\\text{Identity: }a^2-b^2 = (a+b)(a-b)\\(x^4-4)-(x^3+2x) = 0\\(x^2+2)(x^2-2)-x(x^2+2) = 0\\(x^2+2)(x^2-2-x) = 0\\(x^2+2)(x^2-x-2) = 0\\(x^2+2)(x^2-2x-+x-2) = 0\\(x^2+2)((x(x-2)+1(x-2))=0\\(x^2+2)(x+1)(x-2)=0\\\text{Identity: }a^2-b^2 = (a+b)(a-b)\\(x^2-(\sqrt{-2})^2)(x+1)(x-2)=0\\(x+i\sqrt2)(x-i\sqrt2)(x+1)(x-2)=0$