In an increasing sequence of 8 consecutive integers, the sum of the last 4 integers is 822. What is the sum of the first 4 integers in the sequence?
Choose the correct choice
A) 800	B) 808	C) 806	D) 802	E) 804
Solution:   In solving this problem we must first remember that when we have 8 consecutive integers we can display them in terms of just 1 variable. Thus, we have the following:   Integer 1: x   Integer 2: x + 1   Integer 3: x + 2   Integer 4: x + 3   Integer 5: x + 4   Integer 6: x + 5   Integer 7: x + 6   Integer 8: x + 7   We are given that the sum of the first 4 integers is 570. This means that:   x+7+ x+6 + x+5 + x+4 = 822   4x + 22 = 822   4x = 800   x = 200   The sum of the last 4 integers can be expressed and simplified as:   x+ x+1 + x+2+ x+3 = 4x + 6   Substituting 141 for x yields:   (4)(200) + 6 = 806   Answer: 806
<result>C</result>
In an increasing sequence of 8 consecutive integers, the sum of the last 4 integers is 822. What is the sum of the first 4 integers in the sequence?