In an A.P., if `S_(n) = n(4n + 1),` then the value of `S_(20)` is

Options

A. 1610
B. 1520
C. 1620
D. 1400

Answer

To find the value of \( S_{20} \) in the given arithmetic progression where \( S_n = n(4n + 1) \), we will follow these steps:

### Step 1: Understand the formula for \( S_n \)
The formula for the sum of the first \( n \) terms of the arithmetic progression is given as:
\[ S_n = n(4n + 1) \]

### Step 2: Substitute \( n = 20 \) into the formula
To find \( S_{20} \), we will substitute \( n = 20 \) into the formula:
\[ S_{20} = 20(4 \cdot 20 + 1) \]

### Step 3: Calculate \( 4 \cdot 20 + 1 \)
First, we calculate \( 4 \cdot 20 \):
\[ 4 \cdot 20 = 80 \]
Now, add 1:
\[ 80 + 1 = 81 \]

### Step 4: Multiply by 20
Now, we substitute back into the equation for \( S_{20} \):
\[ S_{20} = 20 \cdot 81 \]

### Step 5: Calculate \( 20 \cdot 81 \)
Now, we perform the multiplication:
\[ 20 \cdot 81 = 1620 \]

### Conclusion
Thus, the value of \( S_{20} \) is:
\[ \boxed{1620} \]

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