Calculate the value of each expression where:

x
1
x
1
​
= 5

x
2
x
2
​
= 15

x
3
x
3
​
= 3

x
4
x
4
​
= 3

x
5
x
5
​
= 8

x
6
x
6
​
= 10

x
7
x
7
​
= 12

Scenario:
n
n

Service Model:

Scenario:
∑
i
=
1
n
x
i
i=1
∑
n
​
x
i
​

Service Model:

Scenario:
∑
j
=
2
7
x
j
+
6
j=2
∑
7
​
x
j
​
+6

Service Model:

Scenario:
x
5
x
5
​

Service Model:

Scenario:
∑
i
=
3
6
x
i
n
−
1
n−1
i=3
∑
6
​
x
i
​

​

Service Model:

Draggable item a1499815365658 was dropped.
Match The Notation
For this quiz, you will be matching the notation attached to the letters below to the corresponding numeric value to make sure you understand exactly what is being done with each part of the notation.

Let's break down and solve each of these mathematical scenarios step by step.

### Given values:

\[
x_1 = 5, \quad x_2 = 15, \quad x_3 = 3, \quad x_4 = 3, \quad x_5 = 8, \quad x_6 = 10, \quad x_7 = 12
\]

Now, let's calculate the value of each expression.

### 1. Expression 1: \( \sum_{i=1}^{n} x_i \)

This represents the summation of the values from \( x_1 \) to \( x_n \). Assuming \( n = 7 \), we will sum all values of \( x_i \) from \( x_1 \) to \( x_7 \):

\[
\sum_{i=1}^{7} x_i = x_1 + x_2 + x_3 + x_4 + x_5 + x_6 + x_7
\]

\[
= 5 + 15 + 3 + 3 + 8 + 10 + 12 = 56
\]

So, the value of \( \sum_{i=1}^{7} x_i = 56 \).

---

### 2. Expression 2: \( \sum_{j=2}^{7} x_j + 6 \)

This represents the summation of the values from \( x_2 \) to \( x_7 \), and then adding 6 to the result:

\[
\sum_{j=2}^{7} x_j + 6 = x_2 + x_3 + x_4 + x_5 + x_6 + x_7 + 6
\]

\[
= 15 + 3 + 3 + 8 + 10 + 12 + 6 = 57
\]

So, the value of \( \sum_{j=2}^{7} x_j + 6 = 57 \).

---

### 3. Expression 3: \( x_5 \)

This is simply the value of \( x_5 \), which is 8.

So, \( x_5 = 8 \).

---

### 4. Expression 4: \( \sum_{i=3}^{6} x_i \)

This represents the summation of the values from \( x_3 \) to \( x_6 \):

\[
\sum_{i=3}^{6} x_i = x_3 + x_4 + x_5 + x_6
\]

\[
= 3 + 3 + 8 + 10 = 24
\]

So, the value of \( \sum_{i=3}^{6} x_i = 24 \).

---

### Summary of Results:

1. \( \sum_{i=1}^{7} x_i = 56 \)
2. \( \sum_{j=2}^{7} x_j + 6 = 57 \)
3. \( x_5 = 8 \)
4. \( \sum_{i=3}^{6} x_i = 24 \)

Do you need further details or have any questions about the process?

---

Here are 5 related questions for further exploration:

1. What would \( \sum_{i=1}^{5} x_i \) be, using the same values?
2. How does changing the index limits in a summation affect the final result?
3. What happens if you increase the value of \( x_5 \) in the above expressions?
4. Can you calculate \( \sum_{i=2}^{4} x_i + 10 \)?
5. What is the difference between the sum of \( x_1 \) through \( x_7 \) and the sum of \( x_3 \) through \( x_6 \)?

---

**Tip:** Always check the limits of your summations carefully. Different index ranges lead to different results even when using the same set of numbers!

Calculate the value of each expression where:
x_1 = 5
x_2 = 15
x_3 = 3
x_4 = 3
x_5 = 8
x_6 = 10
x_7 = 12

Scenario: ∑i=1^n xi
Scenario: ∑j=2^7 xj + 6
Scenario: x_5
Scenario: ∑i=3^6 xi

Explore how to calculate the sum of specific expressions using given values for x1 to x7. This problem demonstrates summation notation and arithmetic operations, making it ideal for students in Grades 6-8.

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Scenario: ∑ i

Scenario: ∑ j

Scenario: ∑ i

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