Question

The sum of the first 20 terms of an arithmetic progression is 610. If the first term is 7, what is the common difference?

• A. 3
• B. 5
• C. 4
• D. 6

Hint:

Use the formula $ S_n = \frac{n}{2} [2a + (n-1)d] $ to solve for unknowns in arithmetic progressions.

Answer 1

The Correct Option is B

Given:
First term $ a = 7 $
Number of terms $ n = 20 $
Sum of first 20 terms $ S_{20} = 610 $
Formula for sum of first $ n $ terms of an AP: \[ S_n = \frac{n}{2} \left[ 2a + (n-1)d \right] \]
Substituting values: \[ 610 = \frac{20}{2} \left[ 2(7) + (20 - 1)d \right] \] \[ 610 = 10 \left[ 14 + 19d \right] \]
Dividing both sides by 10: \[ 61 = 14 + 19d \]
Solving for $ d $: \[ 61 - 14 = 19d \Rightarrow 47 = 19d \Rightarrow d = \frac{47}{19} = 5 \]