If `t_n` denotes the nth term of the series 2+3+6+11+18+….. Then `t_50` is

Options

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

Explanation

To find the 50th term \( t_{50} \) of the series \( 2, 3, 6, 11, 18, \ldots \), we first need to identify the pattern in the series and derive a general formula for the nth term.

### Step 1: Identify the terms of the series
The given series is:
- \( t_1 = 2 \)
- \( t_2 = 3 \)
- \( t_3 = 6 \)
- \( t_4 = 11 \)
- \( t_5 = 18 \)

### Step 2: Look for a pattern in the terms
We can express the terms in a different way:
- \( t_1 = 0^2 + 2 \)
- \( t_2 = 1^2 + 2 \)
- \( t_3 = 2^2 + 2 \)
- \( t_4 = 3^2 + 2 \)
- \( t_5 = 4^2 + 2 \)

From this, we can see that:
- \( t_n = (n - 1)^2 + 2 \)

### Step 3: Write the general formula for the nth term
Thus, the general term \( t_n \) can be expressed as:
\[ t_n = (n - 1)^2 + 2 \]

### Step 4: Calculate the 50th term
Now, we need to find \( t_{50} \):
\[ t_{50} = (50 - 1)^2 + 2 \]
\[ t_{50} = 49^2 + 2 \]

### Step 5: Calculate \( 49^2 \)
Calculating \( 49^2 \):
\[ 49^2 = 2401 \]
So,
\[ t_{50} = 2401 + 2 = 2403 \]

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