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: Recall the formula for the sum of an arithmetic progression (AP):

The sum of the first \( n \) terms of an arithmetic progression is given by the formula:

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

Step 2: Identify the values from the given arithmetic progression:

• First term \( a = 2 \)
• Common difference \( d = 5 - 2 = 3 \)
• Number of terms \( n = 20 \)

Step 3: Substitute the values into the sum formula:

Substituting the values into the formula:

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

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

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

Conclusion:

The sum of the first 20 terms of the arithmetic progression is 610. However, none of the provided options (400, 420, 440, or 460) match the calculated result, indicating a possible issue with the options.