In the sequence 2,6,10,....; find the number of terns n if the nth term is 198.
*
2 puntos
48
49
50
52

To solve this problem, we first recognize that the given sequence \(2, 6, 10, \dots\) is an arithmetic sequence. In an arithmetic sequence, the difference between consecutive terms is constant. Let's identify the components of this arithmetic sequence:

- **First term (a):** \(2\)
- **Common difference (d):** \(6 - 2 = 4\)

The general formula for the \(n\)th term of an arithmetic sequence is:

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

Given that the \(n\)th term is \(198\), we need to find \(n\). So, let's set up the equation:

\[
198 = 2 + (n-1) \cdot 4
\]

Now, we'll solve for \(n\):

\[
198 - 2 = (n-1) \cdot 4
\]

\[
196 = (n-1) \cdot 4
\]

\[
n-1 = \frac{196}{4}
\]

\[
n-1 = 49
\]

\[
n = 49 + 1
\]

\[
n = 50
\]

Therefore, the number of terms \(n\) is \(50\).

**Answer:** The correct option is **50**.

Would you like further details or have any questions? 

Here are five related questions you might find interesting:
1. How do you find the sum of the first 50 terms in this arithmetic sequence?
2. What would be the 25th term of the sequence?
3. If the common difference was 5 instead of 4, what would be the 50th term?
4. How can you determine if a given number is a term in the sequence?
5. What happens if the first term is negative, say -2, with the same common difference?

**Tip:** Always check that you've correctly identified the first term and common difference when solving arithmetic sequence problems.

Learn how to find the nth term of an arithmetic sequence where the 50th term is 198. This problem involves using the formula for arithmetic sequences and determining the number of terms. Suitable for high school students.

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