Mathematics
Mathematics
Problem
The common difference of an arithmetic progression is . Compare the th term with the th term and state which is larger, giving your reason in one sentence.Intuitive explanation
In an arithmetic progression, each term increases or decreases by a fixed amount—the common difference. Since your common difference is (negative), the sequence is decreasing: each successive term is 3 units smaller than the previous one. The th term comes earlier in the sequence than the th term, so it hasn't decreased as much yet, making it larger.
Intuitive explanation
In an arithmetic progression, each term increases or decreases by a fixed amount—the common difference. Since your common difference is (negative), the sequence is decreasing: each successive term is 3 units smaller than the previous one. The th term comes earlier in the sequence than the th term, so it hasn't decreased as much yet, making it larger.