The average of odd numbers up to 100 is · ABC26GN1544
Subject: General Aptitude · Chapter: Average · Exam: S.S.C. 2010
The average of odd numbers up to 100 is
(a)49
(b)49.5
(c)50
(d)50.5
Answer
Answer (as printed): C
Explanation
Sum of odd numbers upto $100=1+3+5+\ldots+99$ $$=\frac{50}{2}[2+(50-1) \times 2]=2500 .$$ $\left[\begin{array}{l}\because \text { Sum of } n \text { terms of an A.P. with } \\ \text { first term } a \text { and common diff. } d=\frac{n}{2}[2 a+(n-1) d]\end{array}\right]$ $$\text { ∴ } \text { Required average }=\frac{2500}{50}=50 .$$
Explanation as extracted from the printed page; notation may be imperfect.