In an increasing sequence of 8 consecutive integers, the sum of the first 4 integers is 570. What is the sum of the last 4 integers in the sequence?
Answers:
A) 585
B) 580
C) 586
D) 587
E) 589
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 + x+1 + x+2 + x+3 = 570   4x + 6 = 570   4x = 564   x = 141   The sum of the last 4 integers can be expressed and simplified as:   x+4 + x+5 + x+6+ x+7 = 4x + 22   Substituting 141 for x yields:   (4)(141) + 22 = 586   Answer: 586
<result>C</result>
In an increasing sequence of 8 consecutive integers, the sum of the first 4 integers is 570. What is the sum of the last 4 integers in the sequence?