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Alex787 [66]
4 years ago
14

Given the sequence -3, 9, -27, 81, -243, ..., find the recursive formula.

Mathematics
1 answer:
ollegr [7]4 years ago
8 0

Answer:

a(1)= -3

a(n)=a(n-1) (-3)

Step-by-step explanation:

hope this helps

You might be interested in
Dados os vetores u = (2, -3, -1) e v = (1, -1, 4) o resultado de (u + v) x ( u - v) é igual a?
RoseWind [281]

The cross product distributes over sums, so we have

[O produto cruzado distribui somas, então temos]

(<em>u</em> + <em>v</em>) × (<em>u</em> - <em>v</em>) = (<em>u</em> × <em>u</em>) + (<em>v</em> × <em>u</em>) + (<em>u</em> × (-<em>v</em>)) + (<em>v</em> × (-<em>v</em>))

(<em>u</em> + <em>v</em>) × (<em>u</em> - <em>v</em>) = (<em>u</em> × <em>u</em>) + (<em>v</em> × <em>u</em>) - (<em>u</em> × <em>v</em>) - (<em>v</em> × <em>v</em>)

The cross product of a vector with itself is the zero vector, so

[O produto vetorial de um vetor com ele mesmo é o vetor zero, então]

(<em>u</em> + <em>v</em>) × (<em>u</em> - <em>v</em>) = <em>0</em> + (<em>v</em> × <em>u</em>) - (<em>u</em> × <em>v</em>) - <em>0</em>

(<em>u</em> + <em>v</em>) × (<em>u</em> - <em>v</em>) = (<em>v</em> × <em>u</em>) - (<em>u</em> × <em>v</em>)

The cross product is anticommutative, meaning that for two vectors <em>u</em> and <em>v</em>,

[O produto vetorial é anticomutativo, o que significa que para dois vetores <em>u</em> e <em>v</em>,]

<em>u</em> × <em>v</em> = - (<em>v</em> × <em>u</em>)

So we end up with

[Então acabamos com]

(<em>u</em> + <em>v</em>) × (<em>u</em> - <em>v</em>) = (<em>v</em> × <em>u</em>) + (<em>v</em> × <em>u</em>)

(<em>u</em> + <em>v</em>) × (<em>u</em> - <em>v</em>) = 2 (<em>v</em> × <em>u</em>)

Given that <em>u</em> = (2, -3, -1) and <em>v</em> = (1, -1, 4), compute the cross product as follows:

[Dados esses vetores, calcule o produto vetorial:]

(1, -1, 4) × (2, -3, -1)

= ((1, 0, 0) - (0, 1, 0) + 4 (0, 0, 1)) × (2 (1, 0, 0) - 3 (0, 1, 0) - (0, 0, 1))

= 2 (1, 0, 0) × (1, 0, 0) - 2 (0, 1, 0) × (1, 0, 0) + 8 (0, 0, 1) × (1, 0, 0)

… … - 3 (1, 0, 0) × (0, 1, 0) + 3 (0, 1, 0) × (0, 1, 0) - 12 (0, 0, 1) × (0, 1, 0)

… … - (1, 0, 0) × (0, 0, 1) + (0, 1, 0) × (0, 0, 1) - 4 (0, 0, 1) × (0, 0, 1)

Recall the definition of the cross product:

[Lembre-se da definição de produto vetorial:]

(1, 0, 0) × (0, 1, 0) = (0, 0, 1)

(0, 1, 0) × (0, 0, 1) = (1, 0, 0)

(0, 0, 1) × (1, 0, 0) = (0, 1, 0)

The product reduces to

[O produto se reduz a]

(1, -1, 4) × (2, -3, -1)

= -2 (0, 1, 0) × (1, 0, 0) + 8 (0, 0, 1) × (1, 0, 0)

… … - 3 (1, 0, 0) × (0, 1, 0) - 12 (0, 0, 1) × (0, 1, 0)

… … - (1, 0, 0) × (0, 0, 1) + (0, 1, 0) × (0, 0, 1)

= 2 (0, 0, 1) + 8 (0, 1, 0) - 3 (0, 0, 1) + 12 (1, 0, 0) + (0, 1, 0) + (1, 0, 0)

= - (0, 0, 1) + 9 (0, 1, 0) + 13 (1, 0, 0)

= (13, 9, -1)

Finally,

[Finalmente,]

(<em>u</em> + <em>v</em>) × (<em>u</em> - <em>v</em>) = 2 (13, 9, -1) = (26, 18, -2)

3 0
2 years ago
A farmer has some sheep. The total weight of these sheep is 114 kg.
mihalych1998 [28]

Answer:

8 sheep total after buying 3 sheep

Step-by-step explanation:

At the beginning,  the farmer had 114 kg of sheep,  bu do not know how many.

let  x = unknown number of sheep at the beginning.

mean weight =   (total weight)/(x + 3)  =  24 kg.

mean weight  of 3  = 26 kg.

Total weight of the 3 sheep together =  3*26 = 78 kg.

mean weight =  ( 114 kg + 78kg) / (x + 3)  = 24  kg.

we can solve for x now.

192 / (x + 3 ) = 24

192/24 = x + 3

x + 3 = 8  sheep total after buying

8 0
3 years ago
Read 2 more answers
How do i factor 2x^2 - 16x + 32 ?
lora16 [44]
2x^2 - 16x + 32 = 2x^2 - 8x - 8x + 32 = 2x(x - 4) - 8(x - 4) = (2x - 8)(x - 4)
4 0
3 years ago
The below shows a square ABCD and an equilateral triangle DPC:
Anastaziya [24]

Answer:

Option B)  Sides of equilateral triangle DPC are equal

Step-by-step explanation:

As given:

DPC is an equilateral triangle

By definition of equilateral triangles: All the three sides of triangle DPC will be equal in length to each other

i.e.

DP=PC=DC

In Nick's proof , justification of DP=PC is option B) Sides of equilateral triangle DPC are equal !

5 0
3 years ago
PLZZZZZZZZ help with thissss!!
Trava [24]

Answer:

25x^2 - 30x + 9

Step-by-step explanation:

(5x - 3)^2 = (5x - 3)(5x - 3) =

= (5x)(5x) + (5x)(-3) + (-3)(5x) + (-3)(-3)

= 25x^2 - 15x - 15x + 9

= 25x^2 - 30x + 9

7 0
3 years ago
Read 2 more answers
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