in the sequence 50,45,40,35 which term is -15?

The sequence you've provided is an arithmetic sequence, where each term decreases by 5. To find the term that equals \(-15\), we can use the formula for the \(n\)-th term of an arithmetic sequence:

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

Where:
- \(a_n\) is the \(n\)-th term,
- \(a_1\) is the first term (which is 50),
- \(d\) is the common difference (which is -5),
- \(n\) is the term number.

We need to find \(n\) such that \(a_n = -15\).

\[
-15 = 50 + (n-1) \cdot (-5)
\]

Now, solve for \(n\):

\[
-15 = 50 - 5(n-1)
\]

\[
-15 = 50 - 5n + 5
\]

\[
-15 = 55 - 5n
\]

\[
5n = 55 + 15
\]

\[
5n = 70
\]

\[
n = \frac{70}{5} = 14
\]

So, the 14th term of the sequence is \(-15\).

Would you like more details or have any other questions?

Here are 5 related questions:
1. What is the sum of the first 14 terms of this sequence?
2. How would the sequence change if the common difference was -10 instead of -5?
3. What would be the 20th term of this sequence?
4. How many terms are required for the sequence to reach a value less than \(-100\)?
5. Can you find the general form for the \(n\)-th term of this sequence?

**Tip:** When working with arithmetic sequences, always check if the common difference is positive or negative, as it determines if the sequence is increasing or decreasing.

Learn how to find the nth term of an arithmetic sequence where the terms decrease by 5. This problem involves calculating the term number when the sequence equals -15, using the arithmetic sequence nth-term formula. Suitable for Grades 7-9.

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