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4 years ago

Write an explicit rule for the geometric sequence 4, 8, 16, 32, ..

Mathematics

2 answers:

Alina [70]4 years ago

8 0

8÷4=2
16÷8=2
32÷16=2
multiply by 2

Paul [167]4 years ago

5 0

First term: a(1) = 4; common ratio: r = 2

Then:

a(n) = 4(2)^(n-1)

Check: Predict the 4th term using this formula:

a(4) = 4(2)^3 = 4(8) = 32 (correct)

You might be interested in

What is the ratio 25 to 45 as a simplified fraction

fenix001 [56]

Reducing the fractions, it is also true that:
Part A = 5/14 of the whole
Part B = 9/14 of the whole

6 0

3 years ago

The Garden Task

Igoryamba

If the perimeter of the garden is (14x - 32) ft and has a side length of (x + 2) ft:

the perimeter = 24 ft
the area = 36 sq. ft
if the perimeter of the garden is doubled, the perimeter of the new garden = 48 ft
if the area of the garden is doubled, the area of the new garden = 72 sq. ft

Recall:

A square has equal side lengths
Perimeter of a square = 4(side length)
Area of a square = $(side $ length)^2$

Given:

Perimeter of square (P) = $(14x - 32) $ ft$

Side length (s) = $(x + 2) $ ft$

First, let's find the value of x by creating an equation using the perimeter formula:

Perimeter of a square = 4(side length)

Plug in the values

$(14x - 32) = 4(x + 2)$

Solve for x

$14x - 32 = 4x + 8\\\\14x - 4x = 32 + 8\\\\10x = 40\\\\x = 4$

Find how much fencing would be needed (Perimeter of the fence):

Perimeter of the fence = $(14x - 32) $ ft$

Plug in the value of x

Perimeter of the fence = $14(4) - 32 = 24 $ ft$

Find the area of the garden:

Area of the garden = $(side $ length)^2$

Area = $(x + 2)^2$

Plug in the value of x

Area = $(4 + 2)^2 = 6^2 = 36 $ ft^2$

Find the perimeter if the garden size is doubled:

Perimeter of the new garden = 2 x 24 = 48 ft

Find the area if the garden size is doubled:

Perimeter of the new garden = 2 x 36 = 72 sq. ft

In summary, if the perimeter of the garden is (14x - 32) ft and has a side length of (x + 2) ft:

the perimeter = 24 ft
the area = 36 sq. ft
if the perimeter of the garden is doubled, the perimeter of the new garden = 48 ft
if the area of the garden is doubled, the area of the new garden = 72 sq. ft

Learn more here:

brainly.com/question/13511952

4 0

2 years ago

Use the interactive tool to create the three-dimensional

Sati [7]

The surface area of the three dimensional solid is 72 square centimeters and its three dimensional diagram is attached.

Step-by-step explanation:

The given is,

Detailed view or net diagram of the three dimensional diagram.

Step:1

Three dimensional diagram of the given net diagram is attached.

From the three dimensional diagram given net diagram is rectangular prism.

Step:2

From the three dimensional diagram

Formula for surface area of the rectangular prism,

$A = 2(wl + lh + hw)$ ..............................(1)

Where, w - Width

l - Length

h - Height

From the attachment,

l = 6 cm

w = 2 cm

h = 3 cm

Equation (1) becomes,

$A = 2((6)(2) + (6)(3) + (3)(2))$

= 2 ( 12 + 18 + 6 )

= 2 ( 36 )

A = 72 squared centimeters

( or )

From the net diagram,

Surface area, A = ((6×3)+(2×3)+(2×6)+(2×3)+(3×6)+(2×6))

= 18 + 6 + 12 + 6 + 18 + 12

= 72

Surface area, A = 72 squared centimeters

Result:

The surface area of the three dimensional solid is 72 square centimeters and its three dimensional diagram is attached.

4 0

3 years ago

Read 2 more answers

The area of a circular sun spot is growing at a rate of 1,200 km2/s.

Tpy6a [65]

A)

$\bf \textit{area of a circle}\\\\
A=\pi r^2
\\\\\\
\cfrac{dA}{dt}=\pi \cdot 2r\cfrac{dr}{dt}\implies \cfrac{dA}{dt}=2\pi r\cfrac{dr}{dt}\implies \cfrac{\frac{dA}{dt}}{2\pi r}=\cfrac{dr}{dt}\\\\
-----------------------------\\\\
\left. \cfrac{dr}{dt} \right|_{r=3000}\implies \cfrac{1200}{2\pi \cdot 3000}=\cfrac{dr}{dt}\\\\$

B)

$\bf A=\pi r^2\qquad A=490000\implies 490000=\pi r^2\implies \sqrt{\cfrac{490000}{\pi }}=r
\\\\\\
\left. \cfrac{dr}{dt} \right|_{r=\sqrt{\frac{490000}{\pi }}}\implies \cfrac{1200}{2\pi \cdot \sqrt{\frac{490000}{\pi }}}=\cfrac{dr}{dt}
$

8 0

3 years ago

Find a polynomial that describes the area of the lawn which kevin has to mow in his front yard 6x+5,4x-9

Likurg_2 [28]

Answer:

$Area=24x^2-34x-45$