Call the smallest unknown integer of the consecutive set "n" and call the following integers "n+1," "n+2" and so on for as many integers there are in the set. For example, if the subject of an SAT question is a set of four consecutive positive integers, call them "n," "n+1," "n+2" and "n+3."
Plug the variables into the given algebraic equation. For instance, if the SAT question states that the sum of the squares of four consecutive positive integers is 126, you set up the equation n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 = 126.
Simplify the equation and solve for "n." For example, you can simplify the equation n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 = 126 to 4n^2 + 12n^2 - 112 = 0 by expanding the squared expressions and combining like terms.
If you use your calculator or the quadratic formula, you will find the two solutions are n = 4 and n = -7. Since the question restricts you to positive integers only, you can disregard n = -7. Therefore the smallest integer in the set is 4.
Use the value of "n" to find the rest of the integers in the set. Following the example, if n = 4, then the other numbers are 5, 6 and 7.
Use the values of the consecutive integers to answer the main question in the SAT problem. For example, suppose the full question is "The sum of the squares of four consecutive positive integers is 126. What is the product of the four integers?" Since the four consecutive integers are 4, 5, 6 and 7, and 4*5*6*7 = 840, the answer to this problem is 840.