What is the eighth number in a sequence that starts with $125$ and decreases by $10$ in each step?

The given sequence starts with $ 125 $ and decreases by $ 10 $ at each step. This is an arithmetic sequence with the first term $ a = 125 $ and a common difference $ d = -10 $.

To find the eighth term, we use the formula for the $ n $-th term of an arithmetic sequence:

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

For the eighth term ($ n = 8 $):

\[
a_8 = 125 + (8 - 1) \cdot (-10)
\]

\[
a_8 = 125 + 7 \cdot (-10)
\]

\[
a_8 = 125 - 70
\]

\[
a_8 = 55
\]

So, the eighth term of the sequence is $ \boxed{55} $.

Would you like more details or have any questions?

Here are some related questions to consider:

1. What is the 15th term of this sequence?
2. What is the sum of the first 8 terms of this sequence?
3. How many terms are there in this sequence until it reaches zero or below?
4. What is the formula for the $ n $-th term of this sequence?
5. How would the sequence change if the decrease were by $ 20 $ instead of $ 10 $?

**Tip:** For arithmetic sequences, knowing the first term and common difference allows you to find any term in the sequence easily using the general formula.

Learn how to find the eighth number in an arithmetic sequence that starts with 125 and decreases by 10 at each step. This problem covers arithmetic sequences, including the formula for the n-th term. Suitable for students in Grades 7-9.

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