The given series is an arithmetic sequence, where each term decreases by a constant value.

**First term (\(a_1\))**: \(10\)  
**Common difference (\(d\))**: \(6 - 10 = -4\)

To find the \(n\)th term of an arithmetic sequence, we use the formula:

\[
a_n = a_1 + (n - 1) \times d
\]

Given that \(a_n = -46\), we substitute the known values:

\[
-46 = 10 + (n - 1) \times (-4)
\]

Now, solve for \(n\):

1. Subtract 10 from both sides:

\[
-46 - 10 = (n - 1) \times (-4)
\]

\[
-56 = (n - 1) \times (-4)
\]

2. Divide both sides by \(-4\):

\[
n - 1 = \frac{-56}{-4} = 14
\]

3. Add 1 to both sides:

\[
n = 14 + 1 = 15
\]

So, the term \(-46\) is the **15th term** in the series.

Would you like more details on how this was calculated or any related questions?

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Here are 5 related questions:
1. What is the sum of the first 15 terms of this arithmetic sequence?
2. How would you find the 20th term in the same sequence?
3. What is the formula for the sum of an arithmetic sequence?
4. Can you find the difference in terms if we reverse the sequence?
5. How would you find the number of terms required to reach a specific negative value?

**Tip:** In an arithmetic sequence, if the common difference is negative, the sequence will eventually reach negative values.

Learn how to find the term -46 in the arithmetic sequence 10, 6, 2. Understand the arithmetic sequence nth term formula and step-by-step calculation. Suitable for Grades 7-9.

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