If the sum of n terms of a sequence is given by `S_(n)=3n^(2)-2nAA n in N`, then its 10th term is

Options

A. (a) 55
B. (b) 60
C. (c) 65
D. (d) 59

Answer

To find the 10th term of the sequence where the sum of the first n terms is given by \( S_n = 3n^2 - 2n \), we can follow these steps:

### Step 1: Understand the relationship between the sum and the terms
The nth term of the sequence, denoted as \( A_n \), can be calculated using the formula:
\[ A_n = S_n - S_{n-1} \]
This means that the nth term is the difference between the sum of the first n terms and the sum of the first \( n-1 \) terms.

### Step 2: Calculate \( S_{10} \)
Using the formula for \( S_n \):
\[ S_{10} = 3(10^2) - 2(10) \]
Calculating this:
\[ S_{10} = 3(100) - 20 = 300 - 20 = 280 \]

### Step 3: Calculate \( S_{9} \)
Now, we calculate \( S_{9} \):
\[ S_{9} = 3(9^2) - 2(9) \]
Calculating this:
\[ S_{9} = 3(81) - 18 = 243 - 18 = 225 \]

### Step 4: Find the 10th term \( A_{10} \)
Now we can find \( A_{10} \):
\[ A_{10} = S_{10} - S_{9} \]
Substituting the values we calculated:
\[ A_{10} = 280 - 225 = 55 \]

### Conclusion
Thus, the 10th term of the sequence is:
\[ \boxed{55} \]