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
