Find the sum of all the positive multiples of 7 that are less than 90 (answer format: Interger no units)

To find the sum of all positive multiples of 7 that are less than 90, we first identify those multiples. 

The positive multiples of 7 that are less than 90 are:
\[ 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84 \]

This sequence forms an arithmetic series where:
- The first term \( a_1 = 7 \)
- The common difference \( d = 7 \)
- The last term \( a_n = 84 \)

The number of terms \( n \) in this arithmetic sequence can be calculated using the formula for the \( n \)-th term of an arithmetic sequence:
\[
a_n = a_1 + (n-1) \times d
\]
Plugging in the values:
\[
84 = 7 + (n-1) \times 7
\]
\[
84 - 7 = (n-1) \times 7
\]
\[
77 = (n-1) \times 7
\]
\[
n-1 = 11
\]
\[
n = 12
\]
So, there are 12 terms.

The sum \( S_n \) of an arithmetic series can be calculated using the formula:
\[
S_n = \frac{n}{2} \times (a_1 + a_n)
\]
Substituting the known values:
\[
S_{12} = \frac{12}{2} \times (7 + 84)
\]
\[
S_{12} = 6 \times 91
\]
\[
S_{12} = 546
\]

So, the sum of all the positive multiples of 7 that are less than 90 is \( \boxed{546} \).

Would you like to go over any details, or do you have any questions?

Here are five related questions:
1. How would you find the sum of multiples of 7 that are less than 150?
2. Can you find the sum of all multiples of 5 that are less than 100?
3. How would you modify the method if asked for multiples of a different number?
4. What would be the sum of all positive multiples of 8 less than 80?
5. Can you determine the average of the multiples of 7 less than 90?

**Tip:** When working with arithmetic sequences, always double-check the number of terms and common difference to ensure accuracy.

Find the sum of all the positive multiples of 7 that are less than 90 (answer format: Integer no units).

Learn how to find the sum of all positive multiples of 7 that are less than 90. This arithmetic sequence problem covers important concepts such as summation formulas and sequence terms, suitable for students in Grades 6-8.

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