What will be the digit in the tens place of the sum of the following expression: 7 + 77 + 777 + 7777 + ... + 7777777777777777777

1. (The same as if you added 5x7 and 4x70) The numbere in the 100's and higher places don't contribute to the amount in the tens place

3

To find the digit in the tens place of the sum of the expression, we need to focus on the tens places of each number being added.

Let's examine the pattern of the numbers in the expression:

7
77
777
7777
...
7777777777777777777

We can observe that the number of 7's in each term increases by one compared to the previous term.

To find the sum of these numbers, we can consider the tens places individually.

Step 1: Find the sum of the tens places for each term:
In the first term, 7, the tens place is 0.
In the second term, 77, the tens place is 7.
In the third term, 777, the tens place is 7.
In the fourth term, 7777, the tens place is 7.
...
In the last term, 7777777777777777777, the tens place is 7.

Step 2: Add the values of the tens places from each term:
0 + 7 + 7 + 7 + ... + 7

To simplify the addition, we can use multiplication:
7 multiplied by the number of terms.

Step 3: Determine the number of terms:
The number of terms is equal to the number of 7's in the last term.
In this case, the last term is 7777777777777777777, which has 19 7's.

Therefore, the number of terms is 19.

Step 4: Calculate the sum:
7 * 19 = 133

So, the sum of the tens places is 133.

Lastly, we need to find the digit in the tens place of this sum, which is the remainder when the sum is divided by 10. In this case, 133 % 10 = 3.

Therefore, the digit in the tens place of the given expression is 3.