The given sequence is: 6, 10, 14, 18, ...

This is an arithmetic sequence where:

• The first term ($a_1$) is 6.
• The common difference ($d$) is 4 (since $10 - 6 = 4$).

The formula for the $n$-th term ($a_n$) of an arithmetic sequence is:

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

Substitute the known values into the formula to find the 125th term ($a_{125}$):

$a_{125} = 6 + (125 - 1) \cdot 4$ $a_{125} = 6 + 124 \cdot 4$ $a_{125} = 6 + 496 = 502$

Thus, the 125th term in the sequence is 502.

Would you like further details, or do you have any questions? Here are 5 related questions to think about:

1. What is the 50th term in the same sequence?
2. How do you find the sum of the first 125 terms of this arithmetic sequence?
3. If the common difference was 5 instead of 4, what would the 125th term be?
4. Can you derive the general formula for the sum of an arithmetic sequence?
5. What are the first 10 terms of the sequence with the same common difference but a different starting value, say 8?

Tip: In arithmetic sequences, the difference between consecutive terms is always constant!