If the sum of first n terms of an A.P. is `2n^(2) - n + 1`, then the tenth term of this A.P. is :

Options

A. 36
B. 37
C. 38
D. 39

Explanation

To find the tenth term of the arithmetic progression (A.P.) given that the sum of the first n terms is \( S_n = 2n^2 - n + 1 \), we will follow these steps:

### Step 1: Find the nth term of the A.P.
The nth term \( a_n \) of an A.P. can be calculated using the formula:
\[ a_n = S_n - S_{n-1} \]
where \( S_n \) is the sum of the first n terms and \( S_{n-1} \) is the sum of the first \( n-1 \) terms.

### Step 2: Calculate \( S_{n-1} \)
To find \( S_{n-1} \), we substitute \( n-1 \) into the sum formula:
\[ S_{n-1} = 2(n-1)^2 - (n-1) + 1 \]
Expanding this:
\[ S_{n-1} = 2(n^2 - 2n + 1) - (n - 1) + 1 \]
\[ = 2n^2 - 4n + 2 - n + 1 + 1 \]
\[ = 2n^2 - 5n + 4 \]

### Step 3: Calculate \( a_n \)
Now we can find \( a_n \):
\[ a_n = S_n - S_{n-1} \]
Substituting the values we have:
\[ a_n = (2n^2 - n + 1) - (2n^2 - 5n + 4) \]
\[ = 2n^2 - n + 1 - 2n^2 + 5n - 4 \]
\[ = 4n - 3 \]

### Step 4: Find the 10th term \( a_{10} \)
Now we substitute \( n = 10 \) into the formula for \( a_n \):
\[ a_{10} = 4(10) - 3 \]
\[ = 40 - 3 \]
\[ = 37 \]

### Conclusion
The tenth term of the A.P. is \( \boxed{37} \).

---