The sum of 40 terms of an AP whose first term is 2 and common difference is 4, will be

Options

A. 3200
B. 1600
C. 200
D. 2800

Answer

To find the sum of the first 40 terms of an arithmetic progression (AP) where the first term \( a = 2 \) and the common difference \( d = 4 \), we can use the formula for the sum of the first \( n \) terms of an AP:

\[ S_n = \frac{n}{2} \times (2a + (n - 1)d) \]

### Step-by-step Solution:

1. **Identify the given values:**
- First term \( a = 2 \)
- Common difference \( d = 4 \)
- Number of terms \( n = 40 \)

2. **Substitute the values into the formula:**
\[ S_{40} = \frac{40}{2} \times (2 \times 2 + (40 - 1) \times 4) \]

3. **Calculate \( \frac{40}{2} \):**
\[ \frac{40}{2} = 20 \]

4. **Calculate \( 2 \times 2 \):**
\[ 2 \times 2 = 4 \]

5. **Calculate \( (40 - 1) \times 4 \):**
\[ (40 - 1) = 39 \quad \text{and} \quad 39 \times 4 = 156 \]

6. **Add the results from steps 4 and 5:**
\[ 4 + 156 = 160 \]

7. **Multiply the result from step 3 with the result from step 6:**
\[ S_{40} = 20 \times 160 = 3200 \]

### Final Answer:
The sum of the first 40 terms of the AP is \( 3200 \).

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