
Consecutive integers are integers that follow one another: Example: 1,2,3........ 34,35,36....... 9,8, 7,........ Let x represent an integer, x+1 represents the next consecutive integer, x+2 the integer after that and so on...... Consecutive even integers are even integers that follow one another. We have to add 2 to the preceding even integer to get to the next consecutive even integer: Example: 6,8,10........ 342, 344, 346...... 12,10,8...... If x represents the first even integer x+2 represents the second even integer x+4 represents the third even integer and so on........ x, x+2, x+4............... Consecutive odd integers are odd integers that follow one another. Just as even integers we have to add 2 to the preceding odd integer to get to the next consecutive odd integer: Example: 5,7,9........ 341, 343, 345...... 11,9,7...... If x represents the first odd integer x+2 represents the second odd integer x+4 represents the third odd integer and so on........ x, x+2, x+4............... Example: Find two consecutive integers whose sum is 155. Let x = the first integer Let x + 1 = the second integer the sum of two integers is 155 x + x + 1 = 155 2x + 1 = 155 2x = 154 x = 77 x+1 = 77+1 = 78 Answer: The two consecutive integers whose sum is 155 are 77 and 78. Example: Determine three consecutive integers such that twice the sum of the first and second is 27 more than three times the third. Let x = the first integer Let x+1 = the second integer Let x + 2 = the third integer twice the sum of the first and second is 27 more than three times the third: 2(x + x+1) = 3(x+2)+ 27 2(2x+1) = 3x + 6 + 27 4x + 2 = 3x + 6 + 27 4x  3x = 6 + 27  2 x = 33  2 x = 31 x+1 = 32 x+2 = 33 Answer: The three consecutive integers are 31, 32, 33 Example: Find the consecutive positive even integers whose sum is 94. Let x = the first even integer Let x + 2 = second even integer sum of the integers is 94: x + x+2 = 94 2x + 2 = 94 2x = 92 x = 46 x+2 = 48 Example: The sum of two consecutive integers is 25. Find the two numbers. Let n be the first integer Then n + 1 is the second even integer sum of the integers is 25 implies that n + (n + 1) = 25 n + (n + 1) = 25 2n + 1 = 25 2n = 24 n = 12 n + 1 = 13 The two numbers are 12 and 13 Example: The product of two consecutive negative even integers is 24. Find the numbers. Let n be the first integer then n + 2 is the second integer n(n+2) = 24 n^{2} + 2n = 24 n^{2} + 2n  24 = 0 (n+6)(n4)= 0 n = 6 and n = 4 The solutions are n = 6 and n = 4. Since the number we are looking for is a negative the solution is n = 6 n = 6 n + 2 = 6 + 2 = 4 Therefore the two numbers are 6 and 4 Directions: Solve the following equations with three variables. 