Question by Summer Clouds - Discuss with MathYouLike

Summer Clouds moderators

08/07/2017 at 09:33

In the following sequence, there are 10 numbers. Each number has one more 2 than the preceding number:
2, 22, 222, 2222, ............, 2222222222
What is the hundreds digit of the sum of these of these 10 numbers.

List of answers

Phan Thanh Tinh Coordinator 08/07/2017 at 11:11

Consider the sum of first 10 numbers :

The last digit of the sum is : \(2.10=20\equiv0\) (mod 10)

The tens digit of the sum is : \(2.9+2=20\equiv0\) (mod 10)

The hundreds digit of the sum is : \(2.8+2=18\equiv8\) (mod 10)

So,the answer is 8
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NGUYỄN SANH KIÊN 08/07/2017 at 11:30

The last digit of the sum is : $2.10 = 20 \equiv 0$ (mod 10)

The tens digit of the sum is : $2.9 + 2 = 20 \equiv 0$ (mod 10)

The hundreds digit of the sum is : $2.8 + 2 = 18 \equiv 8$ (mod 10)

So,the answer is 8

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