1 + 2 + 3 + ++10=55, ( 11 + 12 + 13 +...........+20)

It seems there might be some confusion in the equation you've written. I'll clarify it for you.

1. The expression "1 + 2 + 3 + ++10 = 55" is likely a mistake. If you meant to add the numbers from 1 to 10, the correct equation should be:
   \[
1 + 2 + 3 + \ldots + 10 = 55.
\]
   
2. For the second part, you want to find the sum of the numbers from 11 to 20. The sum of an arithmetic series is given by the formula:
   \[
\text{Sum} = \frac{n}{2} \times (\text{first term} + \text{last term}),
\]
   where \( n \) is the number of terms.

   Here, the first term is 11, the last term is 20, and the number of terms \( n \) is:
   \[
n = 20 - 11 + 1 = 10.
\]

   Substituting these into the formula, we get:
   \[
\text{Sum} = \frac{10}{2} \times (11 + 20) = 5 \times 31 = 155.
\]

So, the sum of the numbers from 11 to 20 is **155**.

Would you like more details on this, or do you have any questions?

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Here are 5 related questions for you to consider:

1. What is the sum of the numbers from 21 to 30?
2. How would you find the sum of the first 50 natural numbers?
3. What is the sum of all even numbers between 1 and 100?
4. How do you determine the number of terms in a sequence when the first and last terms are known?
5. Can you find the sum of the squares of the numbers from 1 to 10?

**Tip:** When working with arithmetic sequences, remember that the sum can be quickly calculated using the formula \( S = \frac{n}{2} \times (\text{first term} + \text{last term}) \).

Learn how to calculate the sum of numbers from 1 to 10 and from 11 to 20 using arithmetic series formulas. This problem covers basic arithmetic sequences and series, including step-by-step solutions and formula applications. Suitable for students in Grades 7-9.

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