If the difference between the consecutive numbers in the
sequence below is the same, which two numbers should
be placed in the blanks?
19, ___, ___, 37

To solve this problem, we assume that the difference between consecutive numbers in the sequence is constant. The given sequence is:

\[
19, \_\_, \_\_, 37
\]

Let the common difference be \( d \), and let's denote the missing numbers as \( x_1 \) and \( x_2 \).

The sequence can be written as:
\[
19, x_1, x_2, 37
\]

Since the difference between consecutive terms is constant, we can write:

\[
x_1 = 19 + d
\]
\[
x_2 = 19 + 2d
\]
\[
37 = 19 + 3d
\]

Now solve for \( d \):

\[
37 = 19 + 3d
\]
\[
3d = 37 - 19
\]
\[
3d = 18
\]
\[
d = 6
\]

Now we can find \( x_1 \) and \( x_2 \):

\[
x_1 = 19 + 6 = 25
\]
\[
x_2 = 19 + 2(6) = 31
\]

Thus, the two missing numbers are **25** and **31**.

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

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Here are 5 related questions you could explore:
1. What if the common difference was negative instead?
2. How would you find the 6th number in this arithmetic sequence?
3. Can you find the sum of the first 5 terms of this sequence?
4. What is the general formula for finding any term in an arithmetic sequence?
5. How does the concept of a common difference relate to linear equations?

**Tip**: In an arithmetic sequence, the common difference \(d\) is the same between each consecutive term, making it easy to find missing values by adding or subtracting \(d\).

If the difference between the consecutive numbers in the sequence below is the same, which two numbers should be placed in the blanks? 19, ___, ___, 37

Solve the arithmetic sequence problem 19, ___, ___, 37 by identifying the common difference and finding the missing numbers. Learn key concepts such as the arithmetic sequence formula, common difference, and how to solve for missing terms. Suitable for Grades 6-8.

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