**f.**

Summation from j equals 1 to 5 left parenthesis 5 j minus 6 right parenthesis∑j=15(5j−6)equals=enter your response here

​(Type an integer or a simplified​ fraction.)

We are tasked with evaluating the summation:

\[
\sum_{j=1}^{5} (5j - 6)
\]

This means we need to calculate the expression \( 5j - 6 \) for each value of \( j \) from 1 to 5, and then sum the results.

### Step 1: Evaluate each term
- For \( j = 1 \): \( 5(1) - 6 = 5 - 6 = -1 \)
- For \( j = 2 \): \( 5(2) - 6 = 10 - 6 = 4 \)
- For \( j = 3 \): \( 5(3) - 6 = 15 - 6 = 9 \)
- For \( j = 4 \): \( 5(4) - 6 = 20 - 6 = 14 \)
- For \( j = 5 \): \( 5(5) - 6 = 25 - 6 = 19 \)

### Step 2: Sum the results
Now sum all the evaluated terms:

\[
-1 + 4 + 9 + 14 + 19 = 45
\]

Thus, the value of the summation is:

\[
\boxed{45}
\]

Would you like more details or explanations on any of the steps?

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Here are five related questions to extend your understanding:
1. How do you calculate a summation with a general formula?
2. What happens if the upper limit of the summation increases to 10?
3. Can you generalize the formula for summing \( (5j - 6) \) for any upper limit \( n \)?
4. How would you compute the sum if the expression inside was quadratic, like \( 5j^2 - 6 \)?
5. How do arithmetic sequences relate to summations like this?

**Tip**: Always check each term carefully when performing summations to avoid small arithmetic mistakes!

Summation from j equals 1 to 5 left parenthesis 5 j minus 6 right parenthesis∑j=15(5j−6)equals=enter your response here

Explore the calculation of the summation ∑(5j - 6) from j = 1 to 5. This problem introduces summation concepts, basic algebra, and arithmetic sequences. It is suitable for students in Grades 6-8, helping them practice evaluating expressions and summing sequences.

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