To find the value of the 50th term in an arithmetic sequence, we use the formula for the nth term of an arithmetic sequence:

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

Where:

• $a_n$ is the nth term,
• $a_1$ is the first term,
• $d$ is the common difference,
• $n$ is the term number.

Given:

• $a_1 = 6$,
• $d = 3$,
• $n = 50$.

Now, substitute these values into the formula:

$a_{50} = 6 + (50 - 1) \cdot 3$ $a_{50} = 6 + 49 \cdot 3$ $a_{50} = 6 + 147$ $a_{50} = 153$

So, the value of the 50th term is 153.

Would you like further details or clarification?

Here are 5 related questions to deepen your understanding:

1. How do you find the sum of the first 50 terms in this sequence?
2. What is the 100th term of the sequence?
3. How can you determine the number of terms if the last term of the sequence is 300?
4. What is the general formula for the nth term of any arithmetic sequence?
5. How does the common difference affect the growth of an arithmetic sequence?

Tip: In arithmetic sequences, the common difference remains constant, which makes calculating any term straightforward using the formula.