Question

Find the sum of the first 20 terms of the arithmetic progression: \( 2, 5, 8, 11, \dots \).

• A. 400
• B. 610
• C. 440
• D. 460

Hint:

Remember: The sum of the first \( n \) terms of an AP is calculated using the formula \( S_n = \frac{n}{2} [2a + (n-1)d] \).

Answer 1

The Correct Option is B

Step 1: Retrieve the formula for the sum of an arithmetic progression (AP).

The sum of the initial \( n \) terms of an arithmetic progression is calculated using the formula:

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

Step 2: Determine the parameters of the given arithmetic progression.

• The first term is \( a = 2 \).
• The common difference is \( d = 5 - 2 = 3 \).
• The total number of terms is \( n = 20 \).

Step 3: Insert the identified values into the sum formula.

Substituting the parameters into the formula yields:

\[ S_{20} = \frac{20}{2} \left[ 2 \times 2 + (20-1) \cdot 3 \right] \]

\[ S_{20} = 10 \left[ 4 + 57 \right] \]

\[ S_{20} = 10 \times 61 = 610 \]

Conclusion:

The sum of the first 20 terms of the arithmetic progression is calculated to be 610. This result does not align with any of the provided options (400, 420, 440, or 460), suggesting a discrepancy in the given options.