The unit digit of the sum of the first 111 whole numbers is 5. Explanation:
- The first 111 whole numbers are from 0 to 110.
- The sum of these numbers can be calculated using the formula for the sum of an arithmetic progression:
Sum=n2×(a+l)\text{Sum}=\frac{n}{2}\times (a+l)Sum=2n×(a+l)
where n=111n=111n=111 (number of terms), a=0a=0a=0 (first term), and l=110l=110l=110 (last term).
- Substituting the values:
Sum=1112×(0+110)=1112×110=55×111\text{Sum}=\frac{111}{2}\times (0+110)=\frac{111}{2}\times 110=55\times 111Sum=2111×(0+110)=2111×110=55×111
- To find the unit digit, multiply the unit digits of 55 and 111:
- Unit digit of 55 is 5
- Unit digit of 111 is 1 So, unit digit of the product = 5×1=55\times 1=55×1=5.
Therefore, the unit digit of the sum is 5
