If for n sequences `S_(n)=2(3^(n)-1)`, then the third term is

Options

A. A. 18
B. B. 14
C. C. 36
D. D. 48

Answer

To find the third term of the sequence defined by \( S_n = 2(3^n - 1) \), we will follow these steps:

### Step 1: Understand the formula for the sequence
The sequence is given by:
\[ S_n = 2(3^n - 1) \]
This means that for each value of \( n \), we can compute \( S_n \).

### Step 2: Find the nth term of the sequence
The nth term of the sequence, denoted as \( T_n \), can be calculated using the formula:
\[ T_n = S_n - S_{n-1} \]
This gives us the value of the nth term based on the difference between the nth and (n-1)th terms.

### Step 3: Calculate \( S_3 \) and \( S_2 \)
We need to compute \( S_3 \) and \( S_2 \) to find \( T_3 \):
1. Calculate \( S_3 \):
\[ S_3 = 2(3^3 - 1) = 2(27 - 1) = 2 \times 26 = 52 \]
2. Calculate \( S_2 \):
\[ S_2 = 2(3^2 - 1) = 2(9 - 1) = 2 \times 8 = 16 \]

### Step 4: Calculate \( T_3 \)
Now, we can find \( T_3 \):
\[ T_3 = S_3 - S_2 = 52 - 16 = 36 \]

### Final Answer
The third term \( T_3 \) is:
\[ \boxed{36} \]