Write the set `A = {a_(n):n inN,a_(n+1)=3a_(n),a_(1)=1}` in tabular form.

Answer

To write the set \( A = \{ a_n : n \in \mathbb{N}, a_{n+1} = 3a_n, a_1 = 1 \} \) in tabular form, we will follow these steps:

### Step 1: Understand the recursive definition
We are given that:
- \( a_1 = 1 \)
- \( a_{n+1} = 3a_n \)

This means each term in the sequence is three times the previous term.

### Step 2: Calculate the first few terms
Let's calculate the first few terms of the sequence:
- **For \( n = 1 \)**:
\[ a_1 = 1 \]

- **For \( n = 2 \)**:
\[ a_2 = 3a_1 = 3 \times 1 = 3 \]

- **For \( n = 3 \)**:
\[ a_3 = 3a_2 = 3 \times 3 = 9 \]

- **For \( n = 4 \)**:
\[ a_4 = 3a_3 = 3 \times 9 = 27 \]

### Step 3: Continue calculating more terms
We can continue this process to find more terms if needed, but let's stop at \( a_4 \) for now.

### Step 4: Write the set in tabular form
Now we can write the values we have calculated in a tabular form:

\[ \begin{array}{|c|c|} \hline n & a_n \\ \hline 1 & 1 \\ 2 & 3 \\ 3 & 9 \\ 4 & 27 \\ \hline \end{array} \]

### Conclusion
The set \( A \) in tabular form is:

\[ \begin{array}{|c|c|} \hline n & a_n \\ \hline 1 & 1 \\ 2 & 3 \\ 3 & 9 \\ 4 & 27 \\ \hline \end{array} \]