Problem
Problem
Insert three numbers between 5 and 10 so that all five numbers are in arithmetic sequence.Intuitive explanation
You're building an arithmetic sequence where the first term is 5 and the fifth term is 10. The key insight is that in an arithmetic sequence, consecutive terms differ by a constant amount—the common difference . Once you find using the relationship between the first term, last term, and total number of terms, the three missing numbers fall right out. Think of it as dividing the gap evenly.
Intuitive explanation
You're building an arithmetic sequence where the first term is 5 and the fifth term is 10. The key insight is that in an arithmetic sequence, consecutive terms differ by a constant amount—the common difference . Once you find using the relationship between the first term, last term, and total number of terms, the three missing numbers fall right out. Think of it as dividing the gap evenly.