The question in Bengali asks for the $15^{\text{th}}$ term of the sequence $3, 6, 9, \dots$, which is an arithmetic sequence where each term increases by 3.

For an arithmetic sequence, the $n$-th term is given by: $a_n = a + (n - 1) \times d$ where:

• $a$ is the first term,
• $d$ is the common difference,
• $n$ is the term number.

Here:

• $a = 3$,
• $d = 3$,
• $n = 15$.

So, $a_{15} = 3 + (15 - 1) \times 3 = 3 + 14 \times 3 = 3 + 42 = 45.$

The $15^{\text{th}}$ term is 45.

Would you like more details or have any questions?

Here are some related questions for further exploration:

1. How do you find the sum of the first $n$ terms in an arithmetic sequence?
2. What happens to the terms of an arithmetic sequence if the common difference is negative?
3. How can we determine the number of terms between two given terms in an arithmetic sequence?
4. How is an arithmetic sequence different from a geometric sequence?
5. How would you calculate the $n$-th term if the sequence started with a different number?

Tip: In arithmetic sequences, the difference between consecutive terms remains constant, which simplifies finding any term.