Mathematics

When you insert arithmetic means between two numbers, you're creating an arithmetic sequence where the first term is $2$, the last term is $14$, and there are five terms total (the original two plus three new ones). The key insight is that in an arithmetic sequence, consecutive terms differ by a constant amount—so find that common difference, then count forward to locate the second mean you're looking for.

When you insert arithmetic means between two numbers, you're creating an arithmetic sequence where the first term is $2$, the last term is $14$, and there are five terms total (the original two plus three new ones). The key insight is that in an arithmetic sequence, consecutive terms differ by a constant amount—so find that common difference, then count forward to locate the second mean you're looking for.