To solve this problem, let's first analyze the information given:

The 3rd and 4th terms of an arithmetic sequence are 18 and 14, respectively. We are asked to find the 50th term of the sequence.

Step 1: Determine the common difference

In an arithmetic sequence, the difference between consecutive terms is constant. Let the common difference be $d$.

Given:

• 3rd term ($a_3$) = 18
• 4th term ($a_4$) = 14

We know that: $a_4 = a_3 + d$

Substituting the values: $14 = 18 + d$

Solving for $d$: $d = 14 - 18 = -4$

Step 2: Determine the first term of the sequence

Let the first term be $a_1$.

We know that the $n$-th term of an arithmetic sequence is given by: $a_n = a_1 + (n-1) \times d$

For the 3rd term: $a_3 = a_1 + 2d$ $18 = a_1 + 2(-4)$ $18 = a_1 - 8$ $a_1 = 26$

Step 3: Find the 50th term

Using the formula for the $n$-th term: $a_{50} = a_1 + (50-1) \times d$ $a_{50} = 26 + 49 \times (-4)$ $a_{50} = 26 - 196$ $a_{50} = -170$

Therefore, the 50th term of the sequence is $-170$. However, this does not match any of the given options, indicating there may have been an error in interpretation or calculation.

Upon reviewing the options and the problem structure, let's consider the possibility that the sequence in the problem might be incorrectly transcribed. Nevertheless, if the steps are correct, the answer remains $-170$, but we should double-check the problem context or the options provided.

Would you like any further details, or have any questions about this solution?

Here are some follow-up questions you might find helpful:

1. How do arithmetic sequences differ from geometric sequences?
2. What happens if the common difference $d$ is positive?
3. Can you find the 1st term if only the 2nd and 3rd terms are given?
4. What is the sum of the first 50 terms of this arithmetic sequence?
5. How would you find the general formula for the $n$th term if only one term and the common difference are given?

Tip: Always double-check the signs when dealing with arithmetic sequences, as a small mistake in sign can lead to an incorrect solution.