All categories

2 years ago

Write a reclusive rule for the sequence, then give the next two numbers in the sequence 6,1,7,8,15,23

Mathematics

1 answer:

vlabodo [156]2 years ago

5 0

Answer:

aₙ = aₙ₋₁ + aₙ₋₂

where:

a₁ = 6

a₂= 1.

Step-by-step explanation:

We have the sequence:

6, 1, 7, 8, 15, 23, ...

Is easy to see that this sequence works as follows:

You take 2 consecutive numbers, and the next number is the sum of these two.

Then we have:

6 + 1 = 7

1 + 7 = 8

7 + 8 = 15

8 + 15 = 23

Then the n-th term is equal to the sum of the (n - 1) term and the (n - 2) term.

This is written as:

aₙ = aₙ₋₁ + aₙ₋₂

Because in the recursive rule needs two previous terms, we need to specify the two first terms of the sequence.

Then we need to write also:

a₁ = 6

a₂= 1.

You might be interested in

A bicyclist is finishing his repair of a flat tire when a friend rides by with a constant speed of 3.63 m/s. Four seconds later,

castortr0y [4]

From the moment the friend passes the bicyclist, his friend covers a distance over time t of (3.63 m/s)*t.

The bicyclist covers a distance of 1/2*(2.11 m/s^2)*t^2. They meet when these distances are equal:

3.63 t = 1.055 t^2 ==> 1.055 t^2 - 3.63 t = 0

==> t = 0 s or t = 3.44 s

5 0

2 years ago

F(x)= 2x^3- x^2 +x+ 1 is divided by 2x +1.

ololo11 [35]

Answer:

Step-by-step explanation:

x^2

--------------------------------------------------

2x + 1 / 2x^3 - x^2 + x + 1

2x^3 + x^2

-----------------------

0 + x + 1

x + 1

The quotient is x^2 + ------------

2x + 1

8 0

2 years ago

Integers from 1 to 50

aivan3 [116]

...every number between 1 and 50 is an integer

6 0

2 years ago

Graph the piecewise function.

dmitriy555 [2]

I think the graph below is correct.

4 0

2 years ago

Please help i put a picture below

PSYCHO15rus [73]

Answer:

Step-by-step explanation:

This is not nearly as threatening and scary as I first thought it was. You must be in the section in Geometry where you are taught that perimeter of similar figures exist in a one-to-one relationship while areas of similar figures exist in a squared-to-squared relationship. We will use that here.

The area formula for a regular polygon is

$A=\frac{1}{2}ap$ where a is the apothem and p is the perimeter. We are first asked for the area of the polygon, but it would make more sense to find the perimeter first, since we need it to find the area.

P = 5(8) so

P = 40

We are given that the area of the triangle inside that polygon is 22.022 units squared. Knowing that the area formula for a triangle is

$A=\frac{1}{2}bh$ we can sub in what we know and solve to find the height:

$22.022=\frac{1}{2}(8)h$ and

22.022 = 4h so

h = 5.5055 units

It just so happens that the height of that triangle is also the apothem of the polygon, so now we have what we need to find the area of the polygon:

$A=\frac{1}{2}(5.5055)(40)$

which gives us an area of

A = 110.11 units squared.

Here is where we can use what we know about similar figures and the relationships between perimeters and areas. We will set up a proportion with the smaller polygon info on top and the larger info on bottom. We know that the larger is 3 times the smaller, so the ratio of smaller to larger is

$\frac{s}{l}:\frac{1}{3}$

Since perimeter is one-to-one and we know the perimeter of the smaller, we can create a proportion to solve for the perimeter of the larger:

$\frac{s}{l}:\frac{1}{3}=\frac{40}{x}$

Cross multiply to get that the perimeter is 120 units. You could also have done this by knowing that if the larger is 3 times the size of the smaller, then the side measure of the larger is 24, and 24 * 5 = 120. But we used the way we used because now we have a means to find the area of the larger since we know the area of the smaller.

Area exists in a squared-to-squared relationship of the perimeter which is one-to-one. If the perimeter ratio is 1:3, then the area relationship is

$\frac{s}{l}:\frac{1^2}{3^2}$ which is, simplified:

$\frac{s}{l}:\frac{1}{9}$

Since we know the area for the smaller, we can sub it into a proportion and cross multiply to solve for the area of the larger.

$\frac{s}{l} :\frac{1}{9} =\frac{110.11}{x}$

A of the larger is 990.99 units squared

5 0

2 years ago