If the first term of an AP is -5 and the common difference is 2, then the sum of the first 6 terms is

Options

A. 0
B. 5
C. 6
D. 15

Explanation

To find the sum of the first 6 terms of an arithmetic progression (AP) where the first term \( a = -5 \) and the common difference \( d = 2 \), 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 1: Identify the values
Given:
- First term \( a = -5 \)
- Common difference \( d = 2 \)
- Number of terms \( n = 6 \)

### Step 2: Substitute the values into the formula
Substituting \( n = 6 \), \( a = -5 \), and \( d = 2 \) into the formula:

\[ S_6 = \frac{6}{2} \times (2 \times -5 + (6-1) \times 2) \]

### Step 3: Simplify the expression
Calculating each part step by step:

1. Calculate \( 2a \):
\[ 2a = 2 \times -5 = -10 \]

2. Calculate \( (n-1) \):
\[ n - 1 = 6 - 1 = 5 \]

3. Calculate \( (n-1)d \):
\[ (n-1)d = 5 \times 2 = 10 \]

4. Now substitute these values back into the equation:
\[ S_6 = \frac{6}{2} \times (-10 + 10) \]

### Step 4: Final calculation
Now simplify further:
\[ S_6 = 3 \times (0) = 0 \]

Thus, the sum of the first 6 terms of the AP is \( 0 \).

### Final Answer:
The sum of the first 6 terms is \( 0 \).

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