If `t_n` denotes the nth term of the series `2+3+6+11+18+...` then `t_(50)` a.`49^2-1` b. `49^2` c. `50^2+1` d. `49^2+2`

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 will first identify a pattern in the series and derive a formula for the \( n \)-th term \( t_n \).

### Step 1: Identify the pattern in the series

Let's list the terms of the series:
- \( t_1 = 2 \)
- \( t_2 = 3 \)
- \( t_3 = 6 \)
...