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2 years ago

Which of the following represents the general term for the sequence 2, 4, 6, 8, 10, . . .?

Mathematics

2 answers:

vredina [299]2 years ago

7 0

A(n)=a(1)+(n-1)d=
a(n)=2+(n-1)2=2+2n-2=2n

icang [17]2 years ago

5 0

Answer:

Option (b) is correct.

The general term of the sequence is 2n

Step-by-step explanation:

Given : The sequence 2, 4, 6, 8, 10, . . .

We have to find the representation of the general term of the given sequence 2, 4, 6, 8, 10, . . .

Consider the given sequence 2, 4, 6, .....

The general term of an arithmetic sequence is given by $a_n=a+(n-1)d$

where, a = first term

d is common difference

For the given sequence a = 2

and d = 2

Then $a_n=2+(n-1)2=2+2n-2=2n$

Thus, The general term of the sequence is 2n

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Dean took out a 10-year loan for $40,000 at an APR of 4% compounded monthly. What will his balance be after he has made exactly

damaskus [11]

Answer:

The balance be after he has made exactly half of his monthly payments is $56881.4.

Step-by-step explanation:

Given : Dean took out a 10-year loan for $40,000 at an APR of 4% compounded monthly.

To find : What will his balance be after he has made exactly half of his monthly payments?

Solution :

Formula of monthly payment ,

$M=\frac{\text{Amount}}{\text{Discount factor}}$

Discount factor $D=\frac{1-(1+i)^{-n}}{i}$

Where, Amount = $40,000

Rate r= 4% compounded monthly

$i=\frac{4}{100}=0.04$

Time = 10 years

$n=10\times12=120$

Now, put all the values we get,

$D=\frac{1-(1+i)^{-n}}{i}$

$D=\frac{1-(1+0.04)^{-120}}{0.04}$

$D=\frac{1-(1.04)^{-120}}{0.04}$

$D=\frac{1-0.00903}{0.04}$

$D=\frac{0.9909}{0.04}$

$D=24.7725$

$M=\frac{\text{Amount}}{\text{Discount factor}}$

$M=\frac{40000}{24.7725}$

$M=1614.69$

Half of the monthly payment is $807.345

Payment for 10 years is $807.345\times 120=96881.4$

The balance is $96881.4-$40000=$56881.4

Therefore, The balance be after he has made exactly half of his monthly payments is $56881.4.

3 0

2 years ago

Read 2 more answers

On a number line, the coordinates of X, Y, Z, and W are , , , and , respectively. Find the lengths of the two segments be

Arturiano [62]

Complete Question:

On a number line, the coordinates of X, Y, Z, and W are −8, −5, 4, and 6, respectively. Find the lengths of the two segments below. Then tell whether they are congruent. $\overline{XY}$ and $\overline{ZW}$

Answer:

$\overline{XY} = 3$

$\overline{ZW} = 2$

They are not congruent

Step-by-step explanation:

Length of segment XY:

Coordinate of X = -8

Coordinate of Y = -5

$\overline{XY}$ = |-8 -(-5)| = |-8 + 5| = 3

Length of ZW:

Coordinate of Z = 4

Coordinate of W = 6

$\overline{ZW}$ = |4 - 6| = 2

$\overline{XY}$ ≠ $\overline{ZW}$ , therefore, they are not congruent.

3 0

2 years ago

A three-digit number ends in number 7. If you put the number 7 in the first position, the number will increase by 324. Find the

liq [111]

Answer:

<u>The original three-digit number is 417</u>

Step-by-step explanation:

Let's find out the solution to this problem, this way:

x = the two digits that are not 7

Original number = 10x+7

The value of the shifted number = 700 + x

Difference between the shifted number and the original number = 324

Therefore, we have:

324 = (700 + x) - (10x + 7)

324 = 700 + x - 10x - 7

9x = 693 - 324 (Like terms)

9x = 369

x = 369/9

x = 41

<u>The original three-digit number is 417</u>

5 0

2 years ago

a sloth walks 2/5 mile in each 1/3 hour. write a complex fraction to represent the sloths unit rate of speed. then determine the

insens350 [35]

1 1/5 is the answer

5 0

2 years ago

23) An extension ladder forming a 60° angle with the ground is placed against

Pachacha [2.7K]

Answer: the length of the extended ladder is 8√3 feet or 13.9 feet

the distance between the wall and the bottom of the ladder is 4√3 feet or 6.9 feet

Step-by-step explanation:

The ladder forms a right angle triangle with the building and the ground. The length of the ladder represents the hypotenuse of the right angle triangle. The height from the top of the ladder to the base of the building represents the opposite side of the right angle triangle.

The distance from the bottom of the ladder to the base of the building represents the adjacent side of the right angle triangle.

To determine the extended length of the ladder h, we would apply

the Sine trigonometric ratio.

Sin θ = opposite side/hypotenuse. Therefore,

Sin 60 = 12/h

√3/2 = 12/h

h = 12 × 2/√3 = 24√3

h = 24√3 × √3/√3

h = 8√3

To determine the distance between the wall and the bottom of the ladder d, we would apply

the cosine trigonometric ratio.

Cos θ = adjacent side/hypotenuse.

Therefore,

Cos 60 = d/8√3

0.5 = d/8√3

d = 0.5 × 8√3

d = 4√3

3 0

2 years ago