Question

The sum of the first 20 terms of the arithmetic progression 7, 10, 13, ... is:

• A. 470
• B. 710
• C. 670
• D. 770

Hint:

Formula: \( S_n = \frac{n}{2} [2a + (n-1)d] \) is your go-to for sum of an arithmetic series.

Answer 1

The Correct Option is B

To determine the sum of the initial 20 terms of the arithmetic progression (AP) 7, 10, 13, ..., the formula for the sum of the first n terms of an AP is applied:

Sum = \( \frac{n}{2} \times (\text{First term} + \text{Last term}) \)

Here, the First term is \( a = 7 \), and the Common difference is \( d = 10 - 7 = 3 \).

The formula to calculate the n-th term of an AP is:

\( a_n = a + (n-1) \cdot d \)

For the 20th term (where n=20):

\( a_{20} = 7 + (20-1) \cdot 3 \)

\( a_{20} = 7 + 57 = 64 \)

Applying the sum formula:

Sum = \( \frac{20}{2} \times (7 + 64) \)

\( \text{Sum} = 10 \times 71 = 710 \)

The sum of the first 20 terms is 710.