Question Detail
Question
The sum of the first 10th term of an Arithmetic Progression is 50, and the first term is 1. What is the common difference?
Correct Answer
Option A is the correct answer.
Detailed Explanation
The sum of the first n terms of an AP is S_n = n/2 [2a + (n-1)d]. Here, S_10 = 50, a=1, n=10. So 50 = 10/2 [2(1) + (9)d] = 5(2 + 9d). Thus, 10 = 2 + 9d => 9d = 8 => d = 8/9.
Hint
Use the formula: S_n = n/2 * (2a + (n-1)d).