Answer: 2
Step-by-step explanation:
we have the sequence 1, 11, 111, 1111 and so on.
We can write this sequence as:
A0 = 1
An = A(n -1) + 10^n.
such that:
A1 = A0 + 10^1 = 1 + 10 = 11.
A2 = 11 + 10^2 = 11 + 100 = 111.
and we want to find the tens digit of the sum of the first 30 terms.
ok, in the 30 terms, in the units digit we have a 1, so we have:
30*1 = 30
we leave the zero and the 3 goes to the tens place.
For the tens place. the first term does not aport nothing, and the other 29 terms aport a 1, so we have:
tens = 3 + 29*1 = 32
then we leave a 2 here and pass a 3 to the hundreds place.
But we already answered the question, the tens digit in the sum of the first 30 numbers of the sequence is 2.
