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Gennadij [26K]
4 years ago
15

Complete the recursive formula of the geometric sequence 7, -14,28,-56​

Mathematics
2 answers:
svetlana [45]4 years ago
6 0

Answer:

r=-2 an= 7 (-2)^n-1

Step-by-step explanation:

According to my calculations

Ostrovityanka [42]4 years ago
6 0

Answer:

tₙ = -2tₙ₋₁

Step-by-step explanation:

Recursive formulas for geometric sequences are written tₙ = r(tₙ₋₁)

"tₙ" means the "nth term", the term value you are finding

"tₙ₋₁" means the "term before the nth term", or the previous term

"r" means the common ratio

First, we need to find the common ratio, which is by what number the previous term multiplies by to get the next term.

To find this number, divide one of the values by the previous value.

t₃ ÷ t₂      Substitute the values of term 3 and term 2

= 28 ÷ -14     Divide

= -2     Common ratio

tₙ = r(tₙ₋₁)      Substitute the common ratio into the formula

tₙ = -2tₙ₋₁

Example:

If you wanted to get the term after -56, you would logically multiply -56 by 2. Using the formula:

tₙ = -2tₙ₋₁

t₅ = -2t₅₋₁     The term after -56 will be the 5th term

t₅ = -2t₄       The term before term 5 is term 4

t₅ = -2(-56)         Substitute the value of term 4

t₅ = 112

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Jerome, kevin and seth shared a submarine sandwhich. Jerome ate 1/2 of the sandwich , kevin ate 1/3 of the sandwich, and seth at
Paul [167]

Given:

Jerome ate 1/2 of the sandwich , Kevin ate 1/3 of the sandwich, and Seth ate the rest.

To find:

The ratio of jerome's share to kevin's share to seth's share.

Solution:

Jerome ate 1/2 of the sandwich. So,

Jerome's share = \dfrac{1}{2}

Kevin ate 1/3 of the sandwich. So,

Kevin's share = \dfrac{1}{3}

Seth ate the rest. So,

Seth's share = 1-\dfrac{1}{2}-\dfrac{1}{3}

                     = \dfrac{6-3-2}{6}

                    = \dfrac{1}{6}

The ratio of jerome's share to kevin's share to seth's share is:

\dfrac{1}{2}:\dfrac{1}{3}:\dfrac{1}{6}

To simplify the ratio multiply the ratio by 6.

\dfrac{1}{2}\times 6:\dfrac{1}{3}\times 6:\dfrac{1}{6}\times 6

3:2:1

Therefore, the ratio of jerome's share to kevin's share to seth's share is 3:2:1.

8 0
3 years ago
If f (x) = 3x² + 5x – 7 and g(x) = -5x2 - 4x + 1 what is f +g?
natima [27]

Answer:

Use Microsoft Math Solver

Step-by-step explanation:

it helps with all your math problems

7 0
3 years ago
Can someone help me??
Nadusha1986 [10]

Answer:

x = square root of 2

x = -5

Step-by-step explanation:

The main thing to do in all of these problems is to solve for x. In order to do that with four terms, you need to use a different method of factoring: factor by grouping.

Example 1:

f(x) = x^3  + 5x^2 - 2x - 10

We take the first two terms and figure out what we can factor out by seeing what what they have in common. Both terms have a x^2 or greater so take that out.

f(x) = [ x^2 (x + 5) ] + [ -2x - 10 ]

For the third and fourth terms, we see that they have a 2 in common because you can multiply both numbers by 2. HOWEVER, because you have a x + 5 as a multiple in the other factor, you need to make them match up, so you take out a -2 instead of a 2.

f(x) = [ x^2 (x + 5) ] + [ -2 (x + 5) ]

Then you put the terms you factored out into a parenthesis and the ones in parenthesis as another part of the equation.

f(x) = (x^2 - 2) + ( x + 5 )

0 = (x^2 - 2) + ( x + 5 )

0 = (x^2 - 2)

2 = x^2

square root of 2 = x

0 = ( x + 5 )

-5 = x

6 0
4 years ago
Question part points submissions used use newton's method with the specified initial approximation x1 to find x3, the third appr
serious [3.7K]

Set f(x)=2x^3-3x^2+2. Find the tangent line \ell_1(x) to f(x) at the point when x=x_1:

f'(x)=6x^2-6x\implies f'(x_1)=12 (slope of \ell_1)

\implies\ell_1(x)=12(x-x_1)+f(x_1)=12(x+1)-3=12x+9

Set x_2=-\dfrac9{12}, the root of \ell_1(x). The tangent line \ell_2(x) to f(x) at x=x_2 has slope and thus equation

f'(x_2)=\dfrac{63}8\implies\ell_2(x)=\dfrac{63}8\left(x+\dfrac9{12}\right)-\dfrac{17}{32}=7x+\dfrac{151}{32}

which has its root at x_3=-\dfrac{151}{224}\approx-0.6741.

(The actual value of this root is about -0.6777)

5 0
3 years ago
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