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 and as consecutive integers around , we can assign expressions based on the nature of consecutive integers.
Since is in the middle, the numbers around it should be:
- One integer less than , which we will represent as .
- One integer more than , which we will represent as .
Thus, the expressions for and are:
This setup creates three consecutive integers: , , and .
Would you like more details or have any further questions?
Here are some related questions to deepen understanding:
- How would the expressions change if we needed four consecutive integers?
- What if we needed the sequence to decrease instead of increase?
- Can you find the sum of these three consecutive integers in terms of ?
- How does this concept apply if is an even number specifically?
- How would you express three consecutive odd or even numbers?
Tip: Consecutive integer sequences can always be represented by starting with an integer 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
-
Suitable Grade Level
Grade 6