To find the sum of all integers that are multiples of 7 between 60 and 290, follow these steps:

1. Identify the first and last multiples of 7 in the range:

• First multiple of 7: As we previously found, the smallest multiple of 7 greater than or equal to 60 is 63.
• Last multiple of 7: The largest multiple of 7 less than or equal to 290 is 287.

2. List the multiples of 7 in the range:

• The multiples of 7 are: 63, 70, 77, ..., 287.

3. Count the number of multiples of 7:

• The first multiple of 7 in the sequence is $63 = 7 \times 9$.
• The last multiple of 7 in the sequence is $287 = 7 \times 41$.
• The number of terms $n$ is $41 - 9 + 1 = 33$.

4. Use the formula for the sum of an arithmetic sequence:

The sum $S$ of an arithmetic sequence is given by: $S = \frac{n}{2} \times (\text{first term} + \text{last term})$

• Here, $n = 33$, the first term is 63, and the last term is 287.

5. Calculate the sum:

$S = \frac{33}{2} \times (63 + 287) = \frac{33}{2} \times 350 = 33 \times 175 = 5775$

So, the sum of all integers that are multiples of 7 between 60 and 290 is 5,775.

Would you like any more details or have any questions?

Here are some related questions you might find interesting:

1. What is the sum of all multiples of 5 between 50 and 200?
2. How many integers between 1 and 1000 are multiples of both 7 and 11?
3. Find the sum of all multiples of 7 between 1 and 1000.
4. What is the smallest positive integer that is both a multiple of 7 and 9?
5. What is the product of all multiples of 7 between 63 and 287?

Tip: The sum of an arithmetic series can be quickly calculated if you know the first term, last term, and the number of terms.