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2 years ago

Given: an=3+an−1 and a1=5 What is the explicit rule for the arithmetic sequence?

Mathematics

1 answer:

Flura [38]2 years ago

3 0

The explicit rule for the arithmetic sequence for the sequence is a(n) = 3n + 2.

<h3>What is a sequence?</h3>

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have given:

$\rm a_n=3+a_n_-_1$ and

$\rm a_1=5$

$\rm a_n-a_n_-_1= 3$

The above expression represents the common ratio:

d = 3

First term:

a = 5

The explicit rule for the arithmetic sequence:

a(n) = 5 + (n - 1)3

a(n) = 3n + 2

Thus, the explicit rule for the arithmetic sequence for the sequence is a(n) = 3n + 2.

Learn more about the sequence here:

brainly.com/question/21961097

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A decorative window is made up of a rectangle with semicircles at either end. The ratio of AD to AB is 3:2 and AB is 30 inches.

scZoUnD [109]

Answer: The required ratio will be

$84:1034$

Step-by-step explanation:

Since we have given that

Ratio of AD to AB is 3:2

Length of AB = 30 inches

So, it becomes

$2x=30\\\\x=\frac{30}{2}=15\ inches$

So, Length of AD becomes

$3x=3\times 15=45\ inches$

Now, at either end , there is a semicircle.

Radius of semicircle along AB is given by

$\frac{30}{2}=15\ inches$

So, Area of semicircle along AB and CD is given by

$2\times \frac{\pi r^2}{2}\\\\=\frac{22}{7}\times 15\times 15\\\\=\frac{4950}{7}\ in^2$

Radius of semicircle along AD is given by

$\frac{45}{2}=22.5\ inches$

Area of semicircle along AD and BC is given by

$2\times \frac{1}{2}\pi r^2\\\\=\frac{22}{7}\times \frac{45}{2}\times \frac{45}{2}\\\\=\frac{445500}{28}\ in^2$

And the combined area of the semicircles is given by

$\frac{4950}{7}+\frac{445500}{28}\\\\=\frac{465300}{28}\ in^2$

Area of rectangle is given by

$Length\times width\\\\=AD\times AB\\\\=45\times 30\\\\=1350\ in^2$

Hence, Ratio of the area of the rectangle to the combined area of the semicircles is given by

$1350:\frac{465300}{28}\\\\=1350\times 28:465300\\\\=37800:465300\\\\=84:1034$

Hence, the required ratio will be

$84:1034$

8 0

3 years ago

The circumference of Circle K is $\pi$ . The circumference of Circle L is $4\pi$ . Two circles, one labeled "Circle K" and the o

timurjin [86]

Answer:

Step-by-step explanation:

Given the circumference of Circle K = π

circumference of Circle L = 4π

Ratio of their circumferences = Ck/Cl

Ratio of their circumferences = π/4π

Ratio of their circumferences = 1/4 = 1:4

For their radii

C = 2πr

for circle k with circumference π

π = 2πrk

1 = 2rk

rk = 1/2

for circle l with circumference 4π

4π = 2πr

4 = 2r

r = 4/2

rl = 2

ratio

rk/rl = 1/2/2

rk/rl = 1/4 = 1:4

for the areas

Area of a circle = πr²

for circle k

Ak = π(1/2)²

Ak = π(1/4)

Ak = π/4

for circle l

Al = π(2)²

Al = 4π

Ratio of their areas

Ak/Al = π/4/(4π)

Ak/Al = π/16π

Ak/Al = 1/16 = 1:16

3 0

3 years ago

HELP ASAP FOR BRAINLIEST

zaharov [31]

Answer:

6x2+8x−8

Step-by-step explanation:

6x3+26x2+16x−24

x+3

6x3+26x2+16x−24

x+3

2(x+2)(x+3)(3x−2)

x+3

6x2+8x−8

5 0

3 years ago

Is the expression 2f + 4f + 2 – 3 equivalent to 6f – 1? 6f – 1 evaluated at f = 9 is 53. 2f + 4f + 2 – 3 evaluated at f = 9 is a

morpeh [17]

We have that

the expression 2f + 4f + 2 – 3-------> we can group it (2f+4f)+(2-3)
(2f+4f)+(2-3)=(6f-1)
therefore
the expression [2f + 4f + 2 – 3] is equivalent to [6f-1]

if the expression [6f-1] for f=3 is 17
then
the expression [2f + 4f + 2 – 3] for f=3 is also 17

<span>let's check it
</span>[2*3 + 4*3 + 2 – 3]--------> [6+12+2-3]=[20-3]=17------> is ok

6 0

4 years ago

Read 2 more answers

Rewrite the radical expression as an expression with a raſional exponent.

Wittaler [7]

Answer:

Step-by-step explanation:

i took the test. are u a flvs student?

6 0

2 years ago