why would the answer here not be 6? i understand 6 * 1000 = 6000 so unit digit is 0 but 6^10’s unit digit is 6. at first i had thought it was 6^ sum of 1-1000, but the solution had stated it as 6^1000.

Hi,

The unit’s digit only depends on the unit’s digit of the numbers we are adding.

So, here we can also use pattern recognition.

6, unit’s digit is 6

6+6, unit’s digit is 2

6+6+6, unit’s digit is 8

6+6+6+6, unit’s digit is 4

6+6+6+6+6, unit’s digit is 0

So, if you continue this, you can see that it follows a cycle of (6,2,8,4,0). So if the number of terms we add is divisible by 5, then we get the unit’s digit as 0.

Hence, the unit’s digit for sum till 1000th terms will also be 0.

For your approach, we get 6 “at each and every” unit’s digit, as 6 raised to any power has the unit’s digit as 6. So, we will add 6 for 1000 times to get the unit’s digit (i.e. 6*1000). Hence, the 0.

You are considering only one instance of 6^10 getting 6 as the unit’s digit; however, this is true for all the terms.