If `t_(n)` denotes the n th term of the series `2+3+6+1+18+`…….then `t_(50)` is

Options

A. `49^(2)-1`
B. `49^(2)`
C. `50^(2)+1`
D. `49^(2)+2`

Answer

To find the 50th term of the series given by \( t_n \) where the series is \( 2, 3, 6, 1, 18, \ldots \), we first need to identify a pattern or formula for the terms in the series.

### Step 1: Identify the pattern in the series
The given series is:
- \( t_1 = 2 \)
- \( t_2 = 3 \)
- \( t_3 = 6 \)
- \( t_4 = 1 \)
- \( t_5 = 18 \)

Let's analyze the terms:
- The first term is \( 2 \).
- The second term is \( 3 \) (which is \( 2 + 1 \)).
- The third term is \( 6 \) (which is \( 3 \times 2 \)).
- The fourth term is \( 1 \) (which is \( 6 - 5 \)).
- The fifth term is \( 18 \) (which is \( 1 \times 18 \)).

### Step 2: Establish a formula for the nth term
From the video transcript, it suggests a formula for the nth term:
\[ t_n = 2 + (n - 1)^2 \]

### Step 3: Substitute \( n = 50 \) into the formula
Now we will find \( t_{50} \):
\[ t_{50} = 2 + (50 - 1)^2 \]
\[ t_{50} = 2 + 49^2 \]
Calculating \( 49^2 \):
\[ 49^2 = 2401 \]
Now substituting back:
\[ t_{50} = 2 + 2401 = 2403 \]

### Final Answer
Thus, the 50th term \( t_{50} \) is:
\[ \boxed{2403} \]