Math Problem Statement

Write expressions to replace A and B so that the list below shows three consecutive integers, written from smallest to largest, for all integer values of n.

Solution

To express AA and BB as consecutive integers around nn, we can assign expressions based on the nature of consecutive integers.

Since nn is in the middle, the numbers around it should be:

  • One integer less than nn, which we will represent as A=n1A = n - 1.
  • One integer more than nn, which we will represent as B=n+1B = n + 1.

Thus, the expressions for AA and BB are:

  • A=n1A = n - 1
  • B=n+1B = n + 1

This setup creates three consecutive integers: n1n - 1, nn, and n+1n + 1.

Would you like more details or have any further questions?

Here are some related questions to deepen understanding:

  1. How would the expressions change if we needed four consecutive integers?
  2. What if we needed the sequence to decrease instead of increase?
  3. Can you find the sum of these three consecutive integers in terms of nn?
  4. How does this concept apply if nn is an even number specifically?
  5. How would you express three consecutive odd or even numbers?

Tip: Consecutive integer sequences can always be represented by starting with an integer nn and adjusting by increments of 1 (or 2 for consecutive odds/evens).

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Math Problem Analysis

Mathematical Concepts

Consecutive integers
Algebraic expressions

Formulas

A = n - 1
B = n + 1

Theorems

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Suitable Grade Level

Grade 6