Find the sum of all 11 terms of an AP whose middle-most term is 30.
330
Step 1: We are told the AP has 11 terms. So, \(n = 11\).
Step 2: The sum of \(n\) terms of an AP is given by:
\( S_n = \dfrac{n}{2} (\text{first term} + \text{last term}) \).
Step 3: When the number of terms is odd, there is exactly one middle term. For \(n = 11\), the middle term is the \(\dfrac{11+1}{2} = 6^{th}\) term.
Step 4: It is given that this middle term = 30.
Step 5: A property of AP says: The sum of all terms of an AP with an odd number of terms is equal to the number of terms multiplied by the middle term.
So, \( S_{11} = 11 \times 30 \).
Step 6: Multiply: \( 11 \times 30 = 330 \).
Final Answer: \( S_{11} = 330 \).