MATHEMATICS HIGH SCHOOL

Write the first three terms of the series for which tn = 2(n+3). Find the number of terms of the series required to make the sum 228.

Answers

Answer 1

Answer:

Answer:

The first three terms of the series are 8, 10 and 12. The number of terms is 12 to make the sum 228.

Step-by-step explanation:

The series is defined as

$t_n=2(n+3)$

Put n=1.

$t_1=2(1+3)=2* 4=8$

Put n=2.

$t_2=2(2+3)=2* 5=10$

Put n=3.

$t_3=2(3+3)=2* 6=12$

The first three terms of the series are 8, 10 and 12.

It is an arithmetic series. The first terms is 8 and the common difference is

$d=a_2-a_1=10-8=2$

The sum of n terms of an arithmetic series is

$S_n=(n)/(2)[2a+(n-1)d]$

$288=(n)/(2)[2(8)+(n-1)2]$

$288=(2n)/(2)[8+n-1]$

$288=n[n+7]$

$0=n^2+7n-288$

$0=n^2+19n-12n-288$

$0=n(n+19)-12(n+19)$

$0=(n+19)(n-12)$

Equate each factor equal to zero.

$n=-19,12$

The number of terms can not be negative, therefore the value of n must be 12.

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Why is it a good idea to check to see if your answer is reasonable?a. if your answer is reasonable, you have probably done the problem correctlyc. you just need to solve for the variableb. if you understand the problem, you will not need to check your answerd. to get the correct answer, you will need to draw a pictureMark this and return
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The decimal of 10 3/4
Add -3.8 + 9.8 + 5.7

Solve using the substitution method 2x+3y=1 and y=x-8

Answers

(5, -3) IS THE ANSWER.

x=5
y=-3
thats what i got:)

i have a field 60m long and 110 wide going to be paved i ordered 660000000cm cubed of cement how thick must the cement be to cover field

Answers

First find the area of the field
A=WL
A=(110m)(60m)
A=6,600m^2
Now turn the cm into m
becouse 100cm^3=1m^3
660,000,000cm^3=6,600,000m^3
Now find out how many times you can cover the filled
6,600,000m^3/6,600m^2=100m
So it will be 100m thick.
P.S. I'm assuming you meant you jest forgot the m for 110m.

45 minutes to 1 hour to simplest form

Answers

45 minutes : 1 hour

We need to make the units the same! This is crucial! If you do not have the proper units the whole answer is wrong!

45 minutes : 60 minutes

These are both divisible by 15:

3 minutes : 4 minutes

So, the ratio is 3 : 4

Final Answer: 3:4

Here, we need to write a ratio. A ratio compares two quantities.

45 to 1 hour

45:1

Final answer: 45:1

Find the smallest 4-digit number perfect square.

Answers

31*31= 961 is perfect square but it don't respect the sentence

32*32=1024 is the lowest perfect square formed by 4 digits

41)533
What is 533 divided by 41 using Partial Quotients?

Answers

Answer:

Step-by-step explanation:

533÷41=13 just use a calculator

Final answer:

To divide 533 by 41 using the Partial Quotients method, you first determine how many times 41 goes into 533, which is 10 times, then with the remainder, you repeat the process and find 41 goes 3 times. When you add these partial quotients together, you get the final answer: 13.

Explanation:

The problem here is to divide 533 by 41 using the Partial Quotients method.

The first step is to determine how many times 41 can go into 533 without going over. In this case, it's 10 times, because 10*41 is 410, which is less than 533. So, 10 is part of our answer, and we subtract 410 from 533, which gives us 123.

The next step is to repeat this process with the remainder, 123. 41 can go into 123 three times (since 3*41=123) without going over. So, 3 is another part of our answer. Now, we subtract 123 from 123, which equals 0.

Finally, to get the final answer, we add the partial quotients: 10+3=13. So, 533 divided by 41 using the Partial Quotients method is 13.

Learn more about Partial Quotients here:

brainly.com/question/1893702

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Find the size of angle x and explain how you found your answer.Give your answer in degrees ().
63°
X
Q Zoom
134°
Not drawn accurately