Question

The sum of first 20 terms of the A.P. 1, 4, 7, 10, ... is

• A. 500
• B. 540
• C. 590
• D. 690

Hint:

Always identify the values of a, d, and n from the question first. Then, carefully substitute them into the formula. A common mistake is an error in the order of operations (BODMAS/PEMDAS) - calculate the bracket contents completely before multiplying by \(n/2\).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
We need to find the sum of the first 20 terms of a given Arithmetic Progression. We can use the standard formula for the sum of an A.P.

Step 2: Key Formula or Approach:
The formula for the sum of the first \(n\) terms of an A.P. is:
\[ S_n = \frac{n}{2}[2a + (n-1)d] \] where \(S_n\) is the sum of \(n\) terms, \(a\) is the first term, and \(d\) is the common difference.

Step 3: Detailed Explanation:
From the given A.P. 1, 4, 7, 10, ...:
The first term, \(a = 1\).
The common difference, \(d = 4 - 1 = 3\).
The number of terms, \(n = 20\).
Now, substitute these values into the sum formula:
\[ S_{20} = \frac{20}{2}[2(1) + (20-1) \times 3] \] \[ S_{20} = 10[2 + (19) \times 3] \] \[ S_{20} = 10[2 + 57] \] \[ S_{20} = 10(59) \] \[ S_{20} = 590 \]

Step 4: Final Answer:
The sum of the first 20 terms of the A.P. is 590.