# Confirming Final Answer for Sum of Even Numbers Between 1000 and 2000 | 959400"

• brandon26
In summary, the conversation is discussing the number of even numbers between 1000 and 2000 and the formula for calculating the sum of an arithmetic series. The final answer of 959400 is incorrect and there are actually a lot more than 600 even numbers in this range.
brandon26

## Homework Statement

If I was to work out the sum of all the even numbers between 1000 and 2000, am I correct in saying that there are exactly 600 even numbers?
Therefore, is the final answer 959400?

Could someone please confirm this?
Thank you.

## Homework Equations

Sum = n/2[(2a+(n-1)d]
where n is the number of terms, a is the first term and d is the difference between each term.

a=1000
d=2
n=600

Last edited:
brandon26 said:

## Homework Statement

If I was to work out the sum of all the even numbers between 1000 and 2000, am I correct in saying that there are exactly 600 even numbers?
Why would you think there are "exactly 600 even numbers" in 999 consective integers?

Therefore, is the final answer 959400?

Could someone please confirm this?
Thank you.

## Homework Equations

Sum = n/2[(2a+(n-1)d]
where n is the number of terms, a is the first term and d is the difference between each term.

## The Attempt at a Solution

a=1000
d=2
n=600

The answer depends upon whether "between 1000 and 2000" means "including 1000 and 2000" or not.

Another very nice formula for the sum of an arithmetic series is
$$n\left(\frac{a_1+ a_n}{2}\right)$$
where a1[/sup] and an are the first and last numbers in an arithmetic sequence of n numbers. However, there are a lot more than 600 even numbers between 1000 and 2000!

Using the equation provided, we can calculate the sum of all even numbers between 1000 and 2000 as follows:

Sum = 600/2[(2*1000+(600-1)*2]
= 600/2[(2000+1198]
= 600/2[3198]
= 600/2*3198
= 600*1599
= 959400

Therefore, your final answer of 959400 is correct. There are indeed 600 even numbers between 1000 and 2000, and their sum is 959400. This can also be confirmed by manually counting the numbers or by using a calculator. Great job!

## 1. What does it mean to "check" a final answer?

Checking a final answer means to review and verify the accuracy and correctness of the answer. This can involve double-checking the calculations, ensuring all necessary steps were followed, and confirming that the answer makes sense in the context of the problem.

## 2. Why is it important to have someone check my final answer?

Having someone check your final answer can help catch any mistakes or errors that may have been overlooked. It also provides an opportunity for feedback and clarification, which can help improve understanding and accuracy.

## 3. Who can I ask to check my final answer?

You can ask a peer, a teacher, a tutor, or any other qualified individual to check your final answer. It is important to choose someone who is knowledgeable and experienced in the subject matter and can provide accurate feedback.

## 4. How do I know if my final answer is correct?

There are a few ways to determine if your final answer is correct. First, you can use a calculator or other tools to verify your calculations. You can also compare your answer to the given solution or ask someone to check it for you. Additionally, you can check if your answer makes sense in the context of the problem and follows any given guidelines or constraints.

## 5. Can I use technology to check my final answer?

Yes, you can use technology such as calculators or online resources to check your final answer. However, it is important to understand the steps and calculations involved in finding the answer and not solely rely on technology. It is also recommended to have someone else check your answer to ensure accuracy.

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