If the first term of an AP is \(-5\) and the common difference is \(2\), then the sum of the first 6 terms is
0
5
6
15
We are asked to find the sum of the first 6 terms of an Arithmetic Progression (AP).
Step 1: Recall the formula for the sum of the first \(n\) terms of an AP:
\[ S_n = \dfrac{n}{2} \big(2a + (n-1)d \big) \]
where \(a\) = first term, \(d\) = common difference, \(n\) = number of terms.
Step 2: Here, \(a = -5\), \(d = 2\), \(n = 6\).
Step 3: Substitute these values into the formula:
\[ S_6 = \dfrac{6}{2} \big(2(-5) + (6-1)(2) \big) \]
Step 4: Simplify step by step:
\(\dfrac{6}{2} = 3\)
Inside the bracket: \(2(-5) + 5 \cdot 2 = -10 + 10 = 0\)
Step 5: Multiply: \(3 \times 0 = 0\).
Final Answer: The sum of the first 6 terms is 0.