Consecutive integer problems

key notes :

Definition of Consecutive Integers:

  • Consecutive integers are integers that follow each other in sequence.
  • Examples: 1, 2, 3, 4, 5 are consecutive integers.

Identifying Consecutive Integers:

  • If x is an integer, then x + 1, x + 2, x + 3, etc., are consecutive integers.
  • For negative integers: x − 1, x − 2, x − 3, etc., are consecutive integers.

Solving Problems Involving Consecutive Integers:

Example Problem: Find three consecutive integers such that the sum of the first and the third integer is 51.

  • Let the first integer be x.
  • The consecutive integers are x, x + 1, and x + 2.
  • According to the problem: x + (x + 2) = 51.
  • Solve for x: 2x + 2 = 51.
  • 2x = 49.
  • x = 24.5 (This is not an integer, so there is a need for corrections in this example)

Learn with an example

🏫 A set of 4 consecutive integers sums to 74. What is the least of these integers?

  • First write an expression for each integer.
  • First integer: n
  • Second integer: n + 1
  • Third integer: n + 2
  • Fourth integer: n + 3
  • Next write an expression for the sum of the integers and set it equal to 74. Then solve for n.
  • n + (n + 1) + (n + 2) + (n + 3) = 74
    4n + 6 = 74Combine like terms
    4n = 68Subtract 6 from both sides
    n = 17Divide both sides by 4
  • The least integer, n, is 17.

🏫 There are 3 consecutive integers that sum to 273. What is the least of these integers?

  • First write an expression for each integer.
  • First integer: n
  • Second integer: n + 1
  • Third integer: n + 2
  • Next write an expression for the sum of the integers and set it equal to 273. Then solve for n.
  • n + (n + 1) + (n + 2) = 273
    3n + 3 = 273Combine like terms
    3n = 270Subtract 3 from both sides
    n = 90Divide both sides by 3
  • The least integer, n, is 90.

🏫 There are 3 consecutive integers with a sum of 147. What is the least of these integers?

  • First write an expression for each integer.
  • First integer: n
  • Second integer: n + 1
  • Third integer: n + 2
  • Next write an expression for the sum of the integers and set it equal to 147. Then solve for n.
  • n + (n + 1) + (n + 2) = 147
    3n + 3 = 147Combine like terms
    3n = 144Subtract 3 from both sides
    n = 48Divide both sides by 3
  • The least integer, n, is 48.

Let’s practice!🖊️