UPSC CDS 2 2020 Math Paper

We have,
2, 4, 6, …… , 100
So, here n numbers in this A.P. series.
We know that Tn=a+(n−1)d
⇒100=2+(n−1)2
⇒n−1=49
⇒n=50
Since there are 50, an even number of items . Therefore median is the arithmetic mean of (

50

2

)th and (

50

2

+1)th observations.
So, 25th observation =2+(25−1)2=50
& 26th observation =2+(26−1)2=52
Median =

50+52

2

=51