Find the sum of first 20 terms of an A.P. whose first term is 3 and the last term is 57.

Answer

To find the sum of the first 20 terms of an Arithmetic Progression (A.P.) where the first term is 3 and the last term is 57, we can follow these steps:

### Step 1: Identify the given values
- First term (A) = 3
- Last term (L) = 57
- Number of terms (N) = 20

### Step 2: Use the formula for the sum of the first N terms of an A.P.
The formula for the sum of the first N terms (S_N) of an A.P. is given by:
\[ S_N = \frac{N}{2} \times (A + L) \]

### Step 3: Substitute the values into the formula
Now, we will substitute the values we have into the formula:
\[ S_{20} = \frac{20}{2} \times (3 + 57) \]

### Step 4: Simplify the expression
- Calculate \( \frac{20}{2} \):
\[ \frac{20}{2} = 10 \]
- Calculate \( 3 + 57 \):
\[ 3 + 57 = 60 \]
- Now substitute these values back into the equation:
\[ S_{20} = 10 \times 60 \]

### Step 5: Calculate the final result
- Finally, calculate \( 10 \times 60 \):
\[ S_{20} = 600 \]

### Conclusion
The sum of the first 20 terms of the A.P. is **600**.

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