What is the sum of arithmetic series: first term 1 last term 100 with 100 terms?
A
5050
B
4950
C
5000
D
5100
Correct Answer: Option A — 5050
Explanation:
Sum = n/2 × (first + last) = 100/2 × (1+100) = 50×101 = 5050. This famous result was demonstrated by Gauss. Arithmetic series formulas are fundamental for sequences and series questions and appear in problems involving salary increments equal installments and staircase patterns in competitive exams.