UPSC CDS I 2025 Mathematics Paper

We need to find the sum of all 3-digit numbers that give a remainder of 5 when divided by 50 .
Formula used:
Sum of arithmetic progression (AP): Sn=(n∕2)×(a+1)
Where,
a= First term, 1= Last term, n= Number of terms
Calculation:
The 3 -digit numbers that give a remainder of 5 when divided by 50 are: 105,155,205,...,955.
a=105,1=955
Common difference (d)=50
‌n=(1−a)∕d+1
‌⇒n=(955−105)∕50+1
‌⇒n=850∕50+1
‌⇒n=17+1
‌⇒n=18
Sum of all terms:
‌Sn=(n∕2)×(a+1)
‌⇒S18=(18∕2)×(105+955)
‌⇒S18=9×1060
‌⇒S18=9540