the arithmetic mean between two term in an arithmetic sequence is 39 if one of these term is 32 find the other term

In an arithmetic sequence, the arithmetic mean between two terms is the average of those two terms. Let's denote the two terms as \(a_1\) and \(a_2\). The arithmetic mean is given by:

\[
\text{Arithmetic Mean} = \frac{a_1 + a_2}{2}
\]

According to the problem, the arithmetic mean is 39, and one of the terms is 32. Let's assume \(a_1 = 32\) and find \(a_2\):

\[
39 = \frac{32 + a_2}{2}
\]

To solve for \(a_2\), multiply both sides by 2:

\[
78 = 32 + a_2
\]

Now, subtract 32 from both sides:

\[
a_2 = 46
\]

So, the other term is 46.

Would you like a detailed explanation or do you have any questions? Here are some related questions you might find helpful:

1. How can you find the arithmetic mean of three or more terms in a sequence?
2. What is the general formula for the \(n\)th term in an arithmetic sequence?
3. How does the arithmetic mean relate to the concept of a median in a sequence?
4. What is the sum of the first \(n\) terms in an arithmetic sequence?
5. How do you find the common difference in an arithmetic sequence when given two terms?

**Tip:** In any arithmetic sequence, the difference between consecutive terms remains constant, which is a key property in solving related problems.

Learn how to find the arithmetic mean between two terms in an arithmetic sequence with a detailed step-by-step solution. This problem covers arithmetic sequences and the concept of arithmetic mean. Suitable for students in Grades 7-9.

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