All categories

1 year ago

How many terms in the arithmetic sequence(2,4,6,8....) will give sum of 600

Mathematics

1 answer:

andriy [413]1 year ago

8 0

Answer:

24 terms

Step-by-step explanation:

The sum of an arithmetic sequence is the average of the first and last terms, multiplied by the number of terms. The last term is given by ...

an = a1 + (n-1)d

We have a sequence with first term a1 = 2 and common difference d = 2. So the last term is ...

an = 2+ 2(n -1) = 2n

Then the average of first and last terms times the number of terms is ...

Sn = 600 = n(2 + 2n)/2 = n(n+1) . . . . . . close to n²

We can solve the quadratic in n, or we can estimate the value of n as the integer just below the square root of 600.

√600 ≈ 24.5

so we believe n = 24.

_____

<em>Check</em>

S24 = 24·25 = 600 . . . . . . as required.

You might be interested in

Chelsea has 11 times as many art brushes as Monique. If they have 60 art brushes altogether, how many brushes does Chelsea have?

notsponge [240]

Let Monique's number of art brushes be m.
Then, since Chelsea has <span>11 times as many art brushes as Monique, Chelsea has 11m brushes.

Together they have 60 art brushes, so we write the equation:

m+11m=60.

This means that 12m=60, dividing both sides of the equation by 12 we get m=5.

Chelsea has 11m=11*5=55 brushes.

Answer: 55</span>

7 0

1 year ago

Researchers have a sample size of 24 , and they are using the Student's t-distribution. What are the degrees of freedom and how

DerKrebs [107]

Answer:

For this case assuming that the random variable is X

$df = n-1$

And replacing n = 24 we got:

$df = 24-1=23$

And we notate the distribution we got: $X \sim t_{n-1}= t_{23}$

Step-by-step explanation:

Previous concepts

The t distribution (Student’s t-distribution) is a "probability distribution that is used to estimate population parameters when the sample size is small (n<30) or when the population variance is unknown".

The shape of the t distribution is determined by its degrees of freedom and when the degrees of freedom increase the t distirbution becomes a normal distribution approximately.

The degrees of freedom represent "the number of independent observations in a set of data. For example if we estimate a mean score from a single sample, the number of independent observations would be equal to the sample size minus one."

Solution to the problem

For this case assuming that the random variable is X

$df = n-1$

And replacing n = 24 we got:

$df = 24-1=23$

And we notate the distribution we got: $X \sim t_{n-1}= t_{23}$

7 0

1 year ago

Suppose that a system has 5000 grasshoppers. how many hawks would be expected?

aliina [53]

Probably 2500 or less because they dont need that much hawks.

3 0

1 year ago

Mr. Johnson currently has a square garden. It is in his garden and into a range of 5 feet shorter than three times shorter than

Vlad [161]

Answer:

The Dimension of new garden is $25 \ feet\ \times 10\ feet.$

Step-by-step explanation:

Given:

Perimeter of new garden = 70 feet.

Let the length of the new garden be 'l'.

Also Let the width of the new garden be 'w'.

We need to find the dimension of new garden.

Now Given:

Length is 5 feet shorter than three times it width.

framing the equation we get;

$l =3w-5 \ \ \ \ equation\ 1$

Now we know that;

Perimeter of rectangle is equal to twice the sum of length and width.

framing in equation form we get;

$2(l+w)=70$

Now Diving both side by 2 using Division property of equality we get;

$\frac{2(l+w)}2=\frac{70}{2}\\\\l+w =35$

Now Substituting equation 1 in above equation we get;

$3w-5+w=35\\\\4w-5=35$

Adding both side by 5 Using Addition Property of equality we get'

$4w-5+5=35+5\\\\4w=40$

Now Diving both side by 4 using Division property of equality we get;

$\frac{4w}{4}=\frac{40}{4}\\\\w=10\ ft$

Now Substituting the value of 'w' in equation 1 we get;

$l =3w-5\\\\l =3\times10-5\\\\l = 30-5\\\\l= 25\ ft$

Hence The Dimension of new garden is $25 \ feet\ \times 10\ feet.$

3 0

2 years ago

Simplify the following expression into the form a + bi, where a and b are rational numbers.

vagabundo [1.1K]

The answer is -16 - 10i.

Using the distributive property on the first part, we have:
-2i*7--2i*4i + (3+i)(-2+2i)
-14i+8i² +(3+i)(-2+2i)

Using FOIL on the last part,
-14i+8i²+(3*-2+3*2i+i*-2+i*2i)
-14i+8i²-6+6i-2i+2i²
-10i+8i²-6+2i²

Since we know that i = -1,
-10i+8(-1)-6+2(-1)
-10i-8-6-2
-16-10i

7 0

1 year ago

Read 2 more answers