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3 years ago

How many terms are in the arithmetic sequence 1313, 1616, 1919, ……, 7070, 7373?

1 answer:

7 0

To find the number of terms in the arithmetic sequence, we need to use the formula
$a_{n}= a_{1}+(n-1)d$
where $a_{n}$ is the nth number, $a_{1}$ is the first number, n is the number of terms and d is the difference of the two consecutive numbers.
7373 = 1313 + (n - 1)(303)
7373 = 1313 + 303n - 303
7373 = 1010 + 303n
7373 - 1010 = 303n
6363 = 303n
6363 ÷ 303 = n
n = 21

Therefore, there are 21 terms in the arithmetic sequence given.

You might be interested in

A disco ball is shaped like a sphere with a diameter of 16 inches. To the nearest square inch, what is the surface of the disco

Mademuasel [1]

If the diameter is 16 inches, then its radius is half that, r = 8.

$\bf \textit{surface area of a sphere}\\\\
A=4\pi r^2\quad 
\begin{cases}
r=radius\\
-----\\
r=8
\end{cases}\implies A=4\pi 8^2$

5 0

3 years ago

The maximum height of a vehicle that can safely pass under a bridge is 12 feet 5 inches. A truck measures 162 inches in height.

Bumek [7]

<h2>Answer:</h2>

<em><u>The truck cannot pass safely under the bridge. The truck is 13 inches taller than the maximum height.</u></em>

<h2>Step-by-step explanation:</h2>

In the question,

The maximum height of the vehicle which is capable of passing under the bridge is 12 feet and 5 inches.

So,

Now we know that,

1 feet = 12 inches

So,

12 feet = 12 x 12 = 144 inches

So,

Total height of the vehicle which is permissible to pass under the bridge is,

12 feet 5 inches = 144 + 5 = 149 inches

Also,

Height of the truck = 162 inches

Therefore, we can see that the permissible height is smaller than the height of the vehicle.

Height of vehicle which is more than permissible height is by,

162 - 149 = 13 inches

<em><u>Therefore, the truck cannot pass safely under the bridge. The truck is 13 inches taller than the maximum height.</u></em>

7 0

3 years ago

in a class of 37 students,the number of students who like martial art only is double than the number of students who like athlet

yulyashka [42]

Answer:

number of students who like Athletics only = x = 10 students

number of students who like marshal arts only = 2x = 20 students

Step-by-step explanation:

In a class of 37 students, the number of students who like marshal arts only is

double than the number of students who like athletics only. If 3 students like both

and 4 like none of the games, find out how many students like:

i. Marshal arts

ii. Athletics

Total students in the class = 37

number of students who like Athletics only = x

number of students who like marshal arts only = 2x

Number of students who like both = 3

Number of students who like none = 4

Total = athletics + marshal art + both + none

37 = x + 2x + 3 + 4

37 = 3x + 7

37 - 7 = 3x

30 = 3x

x = 30/3

x = 10

number of students who like Athletics only = x = 10 students

number of students who like marshal arts only = 2x

= 2(10)

= 20 students

5 0

3 years ago

A square and a rhombus have the following in common except

KATRIN_1 [288]

A square is a rhombus, but a rhombus is not always a square

3 0

3 years ago

How do you do this ??

svet-max [94.6K]

The purpose of the grid is to help you record possible and impossible combinations. The repeat of the headings 1st, 2nd, 3rd, 4th helps you compare to both shirt color and name.

Each given statement has certain implications. You are expected to be able to determine as many of those as you can, and mark the grid accordingly.

The first statement says two girls slide down before two other girls. This means the first two girls listed cannot be 3rd or 4th in line, and the last two girls listed cannot be 1st or 2nd in line. It also means that none of the named girls is wearing the blue shirt (so Madeline must be wearing it). These implications are marked in the attachment with X and a circled 1, to indicate to you that the first statement was where we got the X. The X is used to signify an impossible combination.

The second statement tells you the purple shirt will not be 3rd or 4th in line, since at least two girls are after it. It tells you that Alexis is not wearing purple or yellow (so must be wearing white), and it tells you that Alexis and the yellow shirt are not first in line. (We alread knew that about Alexis.)

The third statement lets you finish the problem. We just found that Alexis is wearing the white shirt, so it tells you Madeline is 2nd in line and Alexis is 3rd. (Alexis is 3rd or 4th, but so is Lauren. The only way Madeline can be next to Alexis is for Madeline to be 2nd and Alexis 3rd.) The check marks labeled with a circled 3 are the conclusions we drew from statement 3.

Since the yellow shirt is not first, Lauren must be wearing it 4th in line.

The final conclusion is ...

Hanna, purple
Madeline, blue
Alexis, white
Lauren, yellow

Once you have identified a combination, it can help to mark off the others in that row and column (of the group of 4 rows and columns) as being impossible. This can narrow the choices for the others. I didn't do that here because it makes the diagram busier and the sequence of marks less clear.

_____

It is a good idea to check your final answer with the original problem statements to make sure the answer is consistent with them.

7 0

3 years ago