The image you uploaded is asking about an arithmetic progression (AP). The question provides the first term $a_1 = 3$ and the common difference $d = 2$, and is asking to find the value of $a_9$, the 9th term of the AP.

We can use the formula for the nth term of an arithmetic progression:

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

Where:

• $a_n$ is the nth term
• $a_1$ is the first term
• $d$ is the common difference
• $n$ is the position of the term

For this problem, we want to find $a_9$, so we substitute $a_1 = 3$, $d = 2$, and $n = 9$ into the formula:

$a_9 = 3 + (9 - 1) \cdot 2$

Now, calculate the value:

$a_9 = 3 + 8 \cdot 2$ $a_9 = 3 + 16$ $a_9 = 19$

So, the 9th term $a_9$ is $19$, which corresponds to option B.

Let me know if you'd like more details or if you have any questions.

Related Questions:

1. How can you determine the sum of the first $n$ terms of an arithmetic progression?
2. What would happen if the common difference $d$ were negative in this sequence?
3. How do you find the 15th term of an arithmetic progression where $a_1 = 5$ and $d = 4$?
4. Can you describe the relationship between the terms in an arithmetic progression graphically?
5. What happens if the common difference $d$ is zero in an arithmetic progression?

Tip: Practice calculating terms and sums of arithmetic progressions to become more comfortable with the formulas.